AFFDL-TR-78- 169

SIMULATION OF THE DYNAMIC TENSILECHARACTERISTICS OF NYLON PARACHUTE MATERIALS

QRobert E. McCartyRecovery and Crew Station Branch rVehicle Equipment Division

UL L_

November 1978

C-D

LLU

TECHNICAL REPORT AFFDL-TR-78-169Final Report for Period 1 November 1973 - 1 November 1976

Approved for public release; distribution unlimited.

AIR FORCE FLIGHT DYNAMICS LABORATORYAIR FORCE WRIGHT AERONAUTICAL LABORATORIESAIR FORCE SYSTEMS COMMANDWRIGHT-PATTERSON AIR FORCE BASE, OHIO 45433

..- .- --, ,

I

NOTICE

When Gdvernant drawings, specifications, or other data are used for any pur-pose other than in connection with a definitely related Government procurementoperation, the United States Goverment thereby incurs no responsibility nor anyobligation whatsoever; and the fact that the goverment my have formulated,furnished, or in any way supplied the said drawings, specifications, or otherdata, is not to be regarded by implication or otherwise as in any manner licen-sing the holder or any other person or corporation, or conveying any rights orpermission to manufacture, use, or sell any patented invention that may in anyway be related thereto.

This report has been reviewed by the Information Office (OX) and is releasableto the National Technical Information Service (NTIS). At NTIS, it will be avail-able to the general public, including foreign nations.

This technical report has been reviewed and is approved publication.

ROBERT E. McCARTY RICHARD J.! BEKProject Engineer Group Lea

Recovery Systems Dynamic Analysis Group

FOR THE COXMANDER -

DirectorVehicle Equipment Division

"If your address has changed, if you wish to be removed from our miling list,or if the addressee is no longer employed by your organization please notify

AIFDL/FER ,W-PAFB, OR 45433 to help us mintain a current mailing listf.

Copies of this report should not be returned unless return is zequired by se-curity considerations, contractual obligations, or notice on a specific document.AIR PORCE.S780/ January 1979 - 150

UNCLASSIFT~nSE[CUmTY CLASSIFICATION Of THIS PACE (When Date Ente.,ad) _______________

REPORT DOCUMENTATION PAGE BFRE INSUTIORK

~2. GOVT ACCESSION NO. S. IPIENT'S.CATALOG NUMBER

,51MULATION OF THE.PYNAIC JENSILEHARACTERISTICS FIn iepwt_ 73OFJYLON PARACHUTE MATERIALSio -------________

7. AUTH0R(a)S OTATO GATNIOt.

L RobertE. McCa rty

9. PERFORMII 0 ORGANIZATION NAME AND ADDRESS I0. PROGRIA EPROJECT, TASK

Air Force Flight Dynamics Laboratory Project riI

Wright-Patterson Air Force Base, Ohio 45433 Task 2403

I I. CONTROLLING OFFICE NAME AND ADDRESS -a44140

Air Force Flight Dynamics Laboratory O&dW07Wright-Patterson Air Force Base, Ohio 4543318

14. MONITORING AGENCY NAME A ADDRESS4II diferent frm Controlling Office) IS. SECURITY CLASS. (of tis! report)

SCHEDULE

16. DISTRIBUTION STATEMENT (of this Report)

Approved for public release; distribution unlimited.

117. DISTRIBUTION STATEMENT (of the abstrt *eftered n Stock 20, Ii different from. Report)

iS. SUPPLEMENTARY NOTES

It. KEY WORDS (Continue an reverse eide It necessay and identify by block nueber)

Computer ModelsImpactNytlo Properties 4 J-Subroutines

20. U!!STRACT (Continue an tower" eide If necessary and identify' by block numb.,)

The empirical dvelopment of nylon material subroutines for use in computeranalysis of par ute system dynamics is discussed. The subroutinfs account formaterial plas city, creep and hysteresis. They predict peak forcel and strainsaccurately 95%) and are valid over broad ranges of strain rate (three decades)and tensile ad (zero to minimumn breaking strength). The strain rate sensitiv-ity of nylon is shown to be a manifestation of material creep. Previous modelsare simplistic by comparison and have been,in general~unsatisfactory. A package

DD I FOA04. 1473 EDITION OF INOV 65 18OBSOLETE UNCLASSIFIEDSECURITY CLSIC TOO OF THIS PAGE (When, Data Enterd

%CURITY CLASSIFICATION OF THIS PAGKfUI Dole Balm**

of data processing computer programs also developed provides the capability tog ickly generate additional subroutines for similar materials from limited test

ata.

ULSSIFIEDSECURITY CLASSIFICATION OF THIS PAOIEftha. Dale Enl0

FOREWORD

This report describes an in-house work effort conducted

in the Recovery and Crew Station Branch (FER), Vehicle Equip-

ment Division (FE). Air Force Flight Dynamics Laboratory, AirForce Wright Aeronautical Laboratories, Wright-Patterson Air

Force Base, Ohio,uunder Project 2402, "Vehicle Equipment Tech-

nology", Task 240203, "Aerospace Vehicle Recovery and Escape

Subsystems", Work Unit 24020312, "Crew Escape and Recovery

System Performance Assessment".

The work reported herein was performed during the periodof 1 November 1973 to 1 November 1976 by the author,

Mr. Robert E. McCarty (AFFDL/FER), project engineer. The

report was released by the author in March 1978.

ii

.. ... .I i II I

TABLE OF CONTENTS

SECTION PAGE

I INTRODUCTION

1. Background 12. Approach 73. Scope 8

II DATA ACQUISITION1. Methods 10

2. Apparatus 103. Material Samples 124. Static Data 20

5. Creep Data 206. Dynamic Data 217. Data Reduction 23

III DATA ANALYSIS

1. Method 282. Creep 283. Loading Characteristic 324. Plasticity 365. Hysteresis 446. Damping 50

IV COMPUTER SUBROUTINES

1. Data Processing 532. Subroutine Models 56

V RESULTS 59

VI CONCLUSIONS 62VII RECOMMENDATIONS 63

APPENDIX A MODEL/DATA CORRELATION 65APPENDIX B SUBROUTINE LISTINGS 138REFERENCES 161

v

I.M

LIST OF ILLUSTRATIONS

FIGURE PAGE

1 Loading Characteristics of Nylon 2

2 Hysteresis of Nylon 2

3 Plastic Strain of Nylon 3

4 Creep Behavior 4

5 Schematic for Tensile Impact Test Fixture 11

6 Drop Sled and Weight Plates 13

7 Weighted Drop Sled with LVDT Probe, Zero 14

Strain Weight and Load Link

8 Tensile Impact Test Fixture 15

9 Load Link Attachment and Sled Release Mechanism 16

10 Drop Sled Probe in LVDT 17

11 Nylon Cord and Fabric Test Samples 19

12 Test Sample Dimensions 20

13 Typical Creep Strain Data 21

14 Tensile Impact Test Oscillograph Record 24

15 Calibration Error Determination 25

16 Load Calibration Error Correction 25

17 Displacement Calibration Error Correction 26

18 Creep Strain Histories for Fabric 28

19 Creep Strain Model 30

20 Creep Strain Rate Model 31

21 Creep Strain Rate History 32

22 Ideal Creep Test 33

23 Actual Creep Test 33

24 Fabric Fill Loading Characteristics 34

25 Creep Contribution to Total Strain 35

26 Loading Characteristics with Creep Effects 36

Subtracted Out

27 Model with Creep Effect 38

28 Residual Strain as a Function of Maximum 38

Strain

vi

LIST OF ILLUSTRATIONS (Concluded)

FIGURE PAGE

29 Repeated Loading Characteristics 39

30 Initial and Subsequent Loading 41

31 Model with Creep and Plasticity Effects 41

32 Continuous Loading Characteristic 42

33 Residual Strain for Material under Load and 43

under Zero load

34 Representation of Unloading Characteristics 4535 FD versus ELS Data 45

36 Ratioed FD. versus ELS Data 46

37 FD Ratios as a Function of ELMI 4738 Model with Creep, Plasticity, and Hysteresis 48

Effects

39 Model Unloading Discontinuity 49

40 Model with Continuous Loading Term 50

41 VSFD versus Strain Rate 5142 Typical Model-Data Phase Correlation 52

43 Data Processing Flow Diagram 54

vii

LIST OF TABLES

TABLE PAGE

1 Impact Test Fixture Components 182 Tensile Test Parameters 23

3 Load and Displacement Data Calibration 27Errors Assumed

: Viii

LIST OF SYMBOLS

Symbol Units Definition-- 2AX ft/sec Component of relative acceleration

of two end points of tensile memberin the direction parallel the

member. Same as P(l).

CSR(I,J) sec Array of values for creep strainI - 1,6 rate. Used as the dependentJ - 1,3 variable in creep model. It is a

function of both time, TC(I) and

tensile load, FC(J).

DEC sec Current creep strain rate calcu-

lated from TBL2. Differs from

current creep strain rate, P(3),

only by a scalar multiple.

-1DELO sec Strain rate of tensile member based

on original unstressed length of

tensile member, LO.

DELOMAX sec 1 Maximum positive strain rate exper-ienced by tensile member during its

loading history..

DPA(I) Array of abscissae for the six

I - 1,6 fixed knots in the cubic spline fit

used to represent material unload-

ing characteristic.

ix

LIST OF SYMBOLS (Continued)

Symbol Units Definition

DPC(IJ) Array of cubic spline coefficients

I - 1,5 used with DPA(I) and DPO (I) toJ - 1,3 represent material unloading char-

acteristic. DPA(I), DPO(I) and DPC

(I,J) define load FD4 as a function

of normalized strain ELS.

DPO(I) lb for Array of ordinates for the six

I = 1,6 cord fixed knots in cubic spline fitlb/in for used to represent material unload-

fabric ing characteristic.

EC in/in Creep strain in tensile member.

EDOT sec- Initial, maximum strain rate exper-

ienced by tensile member during

drop weight testing.

EL in/in Strain in tensile member based on

original unstressed length, LO.

Includes residual strain, ELR, and

creep strain, EC.

ELM in/in Maximum strain experienced by

tensile member during its loading

history.

ELM1 in/in Maximum strain experienced by

tensile member during the current

loading cycle only.

x

LIST OF SYMBOLS (Continued)

Symbol Units Definition

ELO in/in Strain of tensile member based onoriginal unstressed length, LO.

Includes residual strain, ELR, but

excludes creep strain, EC.

ELOT in/in Linear transform of strain, ELO, in

tensile member. Has the form (ELO-

ELR) ELM/(ELM-ELR).

ELR in/in Residual strain in tensile member.

This plus creep strain, EC, equals

the total plastic strain in tensilemember. Total plastic strain is

that strain exhibited by tensilemember when load is reduced to zero.

ELRL in/in Upper bound for residual strain,

ELR, as a function of maximum

strain, ELM.

ELRR in/in Lower bound for residual strain,

ELR, as a function of maximum

strain, ELM.

ELS Normalized strain used to calculate

load, FD4, during unloading of ten-

sile member. Has the form (ELMl-

ELO)/ (ELMl-ELR).

EXA(I) in/in Array of abscissae for the six fix-

I - 1,6 ed knots in the cubic spline fit

used to represent the material

loading characteristic.

xi

LIST OF SYMBOLS (Continued)

Symbol Units Definition

EXC(I,J) - Array of cubic spline coefficients

I - 1,5 used with EXA(I) and EXO(I) to

J - 1,3 represent the material loading

characteristic. EXA(I), EXO(I) and

EXC(I,J) define the initial tensile

load FSO as a function of strain

ELO, and repeated tensile loads FSR

as a function of the transformedstrain ELOT.

EXO(I) lb for Array of ordinates for the six fixed

I - 1,6 cord knots in the cubic spline fit used

lb/in to represent the material loading

for characteristic.

fabric

FC(I) lb for Array of values for tensile load.

1 1,3 cord Used as one of the independent

lb/in variables in the creep model.

for

fabric

FD lb for The current unloading decrement

cord derived from load FD2. Value

lb/in depends on the relative acceleration

for of tensile member end points, P(l).

fabric When relative acceleration is nega-

tive or zero, FD has the value of

FD2. When relative acceleration is

positive, FD reduces the magnitude

of FD2 by the ratio of current nega-

tive strain rate to maximum negative

xii

LIST OF SYMBOLS (Continued)

Symbol Units Definitionstrain rate. This drives the

unloading decrement to zero asnegative strain rates approach zero.

FDl lb for The same load as FD3 but limited to

cord the value zero whenever strain ratelb/in is zero or positive.

for

fabric

FD2 lb for Same as FDl except that is has the

cord value zero whenever tensile memberlb/in length is less than the current

for unstressed length, L.

fabric

FD3 lb for Value of load FD4 scaled for current

cord cycle maximum strain and modifiedlb/in by a linear viscous damping term.

for It is also limited to values

fabric between zero and the current tensileload, FS. This prevents compression

in flexible members since unloadingdecrements are subtracted from ten-

sile loads to model unloading.

FD4 lb for Load calculated from the cubic

cord spline fit for the material unload-lb/in ing characteristic. DPA(I), DPO(I),

for and DPC(I,J) are required for thefabric calculation of FD4 as a function of

normalized strain, ELS.

xiii

LIST OF SYMBOLS (Continued)

Symbol Units Definition

FS lb for The current load in tensile member

cord during loading. Equal to the value

lb/in of FSl.

for

fabric

FSO lb for Tensile load calculated from the

cord cubic spline fit for the material

lb/in initial loading characteristic.for EXA(I), EXO(I), and EXC(I,J) are

fabric required for the calculation of FSO

as a function of strain, ELO.

FSOL lb for Same as FSO but limited to positive

cord values only.

lb/in

for

fabric

FSR lb for Tensile load calculated from the

cord cubic spline fit for the material

lb/in repeated loading characteristic.for EXA(I), EXO(I), and EXC(I,J) are

fabric required for the calculation of FSR

as a function of the transformed

strain, ELOT.

FSRL lb for Same as FSR but limited to positive

cord values only.

lb/in

for

fabric

xiv4

L ,. I 1-' -

LIST OF SYMBOLS (Continued)

Symbol Units Definition

FSW(A,B,C,D) - External FORTRAN function. Equals B

if A is less than zero, C if A

equals zero, D if A is greater than

zero.

FS1 lb for Same as FS2 but has the value zerocord whenever tensile member length-is

lb/in less than the current unstressed

for length, L.

fabric

FS2 lb for Has the value of FSOL for initial

cord loading of material and the valuelb/in of FSRL for repeated loading of the

for material.

fabric

FT lb for Tensile load. The differencecord between the load FS and the load FD.

lb/in Has the value FS whenever strain

for rate is zero or positive since FD is

fabric zero for these cases.

FTR lb Tensile load FT multiplied by

material width WIDTH. For cords,

webs, and tapes the value is the

same as FT. For fabric, FTR re-presents a total load for a given

width of fabric whereas FT re-presents linear stress in lb/in.

Lg ft2/sec Acceleration of gravity.

xv

LIST OF SYMBOLS (Continued)

Symbol Units Definition

IER Error parameter related to routine

TBL2.

IMODE Alphanumeric parameter used in pro-

gram MADLOT (Section IV.l). Not

required by subroutine model.

KCR A scalar quantity used to alter

the magnitude of P(3) during model

development. Should have the value

1.

KDP A scalar quantity used to alter

the magnitude of FD3 during model

development. Should have the value

1.

KPU A scalar quantity used in program

BOUNCE (Section IV.l) Not required

by subroutine model.

KRL A scalar quantity used to alter the

magnitude of ELR during model devel-opment. Should have the value of 1.

L ft Current unstressed length of tensile

member. Includes residual strain,

ELR. Excludes creep strain, EC.

LO ft Original unstressed length of ten-

sile member.

xvi

.. . .., ...r| II . . - , i , i. .

LIST OF SYMBOLS (Continued)

Symbol Units Definition

M sl Total mass of drop weight sled usedin dynamic tensile testing.

NDX Number of elements in array TC.

Same as NY.

NX Number of elements in array FC.

NY Number of elements in array TC.

P(l) ft/sec 2 Component of relative acceleration

of two end points of tensile member

in the direction parallel the

member.

P(2) ft/sec Component of relative velocity of

two end points of tensi.le member in

the direction parallel the member.

P(3) sec Creep strain rate in tensile member.

RATIO A scalar quantity used to adjust the

magnitude of load, FD3. It is a

cubic polynomial function of the

current cycle peak strain, ELMI.

RLIM(A,B,C) An external FORTRAN function. When

A is less than B, the value of B is

assigned to A. When A is greater

than C, the value of C is assigned

to A.

xvii

LIST OF SYMBOLS (Continued)

Symbol Units DefinitionRMAXD sec-1 Has the value of strain rate DELO

when strain rate is negative.

Arbitrarily assigned the value of-1.E-6 when strain rate is positive.

RMAXD2 sec 1 Maximum negative strain rateexperienced by tensile member

during the current unloading cycle

only.

T sec Current time.

TBL2 Double linear interpolation routine

used to calculate current creepstrain rate from tensile load FT

and cumulative time under load TF.

TC(I) sec Array of values for time. Used as

I - 1,6 one of the independent variables in

the creep model.

TF sec Cumulative time for which tensile

member experienced nonzero load.

TN sec Current Time.

TS sec Cumulative time for which tensile

member experienced zero load.

TSS Ratio of TS to value of relaxation

time for the material. Used to

interpolate value of residual

xviii

LIST OF SYMBOLS (Continued)

Symbol Units Definitionstrain, ELR, between its bounds,

ELRL and ELRR.

TT sec Value of time T when TF was last

calculated.

VSFD Linear function of maximum strainrate, DELOMAX. Used as a linear

viscous damping term in expressionfor load FD3.

VSFDM sec Linear viscous damping coefficient.Used as slope in term for linear

viscous damping, VSFD.

VX ft/sec Component of relative velocity oftwo end points of tensile member inthe direction parallel the member.

WIDTH in Width of fabric samples. Has thevalue of 1.0 for cords, webs, and

tapes.

X ft Length of tensile member includingresidual strain, ELR, and creep

strain, EC.

Y(l) ft/sec Component of relative velocity oftwo end points of tensile member inthe direction parallel the member.

Y(2) ft Length of tensile member.

xix

LIST OF SYMBOLS (Concluded)

Symbol Units Definition

Y(3 in/in Creep strain in tensile member.

I xx

SECTION 1

INTRODUCTION

1. Background

Computer programs have contributed much to the designand analysis of deployable aerodynamic decelerator systems.

Most of the major parachute analysis computer programs devel-

oped over the last decade include in some form a mathematical

model for the properties of the materials comprising the

system. The task of modelling the behavior of parachute mate-

rials in such a manner has come to be regarded as both an

indispensable element in computer analyses and a major road-

block to full success of the same computer analyses. It is

essential because the dynamics of parachute systems prove to

be very sensitive to material properties, and at the same time

becomes an obstacle primarily because the behavior of

parachute materials is so complex.

A review of the typical tensile behavior of the most

widely used parachute material, nylon, will serve to explain

the difficulty encountered in modelling its properties. The

load-strain characteristic, referred to in this report as theloading characteristic, of a nylon tensile member is quite

nonlinear and demonstrates a strong sensitivity to strain rate,

as can be seen from Figure 1. For a parachute structural

member in tension the strain rate is defined to be the differ-

ence between the lengthwise velocity components of the member

ends divided by the length of the meber. It will be reported

in units of sec -I . Positive strain rates imply that the member

is growing longer, negative ones that it is growing shorter.

The word loading will be used to imply positive strain rates,

the word unloading to imply negative strain rates.

During unloading, nylon exhibits strong hysteresis, that

is, it unloads along a characteristic load-strain curve which

is considerably different from the one along which it loads

as illustrated in Figure 2. The area contained by the two

1

0 4 sec7'O strain rote

1. 1 oz. nylonripstop fabric 0.01 sec'

strain rote

.0

-0

q-J

0

Stan(i/n

1. 1 oz. nylonripsiop fabric

T

WLoading UnloadingCharacteristic Characteristic

0

00.0 0.14 0.28

Strain (in/in)

Figure 2. Hysteresis of Nylon.

j 2

characteristics represents the kinetic energy dissipated perunit length of material.

Another significant aspect of nylon tensile behavior isthe large plastic strain exhibited by the material. Figure 3illustrates this. Plastic strain is defined to be that strain

0

400 lbnylon cord

.o0

a 00

0

0.0 B A .12 .24

Stroin (in/in)

Figure 3. Plastic Strain of Nylon.

remaining in a tensile member when the load is zero afterhaving been loaded. Figure 3 indicates that nylon plasticstrain has two components, one time dependent and one not.Immediately upon unloading, the material exhibits the largeplastic strain A. After the passage of some time at zero loadit exhibits the smaller plastic strain B (at the beginningof the second loading cycle). Plastic strain B is independentof time, or permanent. The material process of shrinkingfrom initial strain A to later strain B is referred to asrelaxation.

I

.... Iiii - mr ... .. .... . .. ... .. .. ...... .. .. .

Yst another significant aspect of the tensile properties

of nylon is the presence of creep which is defined as that

strain suffered by the material as a function of time under

static tensile load. Figure 4 depicts typical creep behavior

I Primary CreepII Secondary CreepIII Tertiary Creep high load

,- x Rupture

0I.-

Time

Figure 4. Creep Behavior

including its three stages: primary, secondary, and tertiary.

Primary creep is characterized by decreasing strain rate with

time, secondary by constant minimum strain rate, and tertiary

by rapidly increasing strain rate to the point of material

rupture. The creep strain history can change dramatically

for different static load levels, so in general creep in nylon

is a function of both time and tensile load.

Studies, such as those in References 1 and 2, have shown

that the number of these mechanical properties included in

(1) Priesser , J.S. and Green, G.C., "Effect of SuspensionLine Elasticity on Parachute Loads," Journal of Spacecraft andRockets, Vol. 7, No. 10, Oct. 1970, pp. 1278-1280.

(2) Poole, L.R., "Effect of Suspension-Line Viscous Damping onParachute Opening Load Amplification," Journal of Spacecraftand Rockets, Vol. 10, No. 1, Jan. 1973, pp. 92-93.

4

the mathematical model of a parachute material has a marked

effect upon computer analyses utilizing that model. As has

been mentioned earlier, successful computer analysis of para-

chute systems depends heavily on the availability of realistic

ma-erial math models.

A considerable variety of parachute material computer

models already exist. The simplest, such as that used in

Reference 3, assume that the material is linearly elastic,

i.e., that the loading characteristic is linear and that the

material exhibits no strain rate sensitivity, hysteresis,

plasticity or creep. Others, for example those in References

4, 5, and 6, vary this approach somewhat by assuming a non-

linear elastic model. Some researchers have tried to account

for the effects of hysteresis by assuming the presence of

viscous damping in the material. Modelling this damping com-

ponent of the tensile load as a single constant multiplied by

material strain rate, as in References 7 and 8, implies linear

viscous damping. Allowing a variable coefficient or a matrix

of coefficients to multiply material strain rate implies non-

linear viscous damping. The material model cited in

(3) Mullins, W.M., et al., Investigation of Prediction Methodsfor the Loads and Stresses of Apollo Type Spacecraft Parachutes,Volume 2: Stresses, NASA-CR-134231, 1970.

(4) Houmard, J.E., Stress Analysis of the Viking ParachuteAIAA Paper 73-444, 1973.

(5) Reynolds, D.T.,and Mullins, W.M., An Internal LoadsAnalysis for Ribbon Parachutes, NVR 75-12, Northrop Corp.,Ventura Division, 1975.

(6) McVey, D.F., and Wolf, D.F., "Analysis of Deployment andInflation of Large Ribbon Parachutes," Journal of Aircraft,Vol. 11, No. 2, February 1974, pp. 96-103.

(7) Ibrahim, S.K., and Engdahl, R.A., Parachute Dynamics andStability Analysis, NASA-CR-120326, February 1974.

(8) Sundberg, W., Finite-Element Modelling of ParachuteDeployment and Inflation, AIAA Paper 75-1380, 1975.

5

Reference 9 was used in analysis of the Viking Mars Lander

parachute recovery system deployment and inflation. It

assumed nonlinear viscous damping, nonlinear elasticity and

an arbitrary history of plastic strain. Notwithstanding the

fact that this model was the most sophisticated ever devel-

oped, its authors have written that "Significant voids in

the knowledge of... suspension system physical properties

appear to be a major obstacle to obtaining very accurate

(parachute dynamics) simulations and to the use of the

analytical model in a predictive mode." This theme is

repeated in Reference 10: "A continuing effort is needed to

obtain data ... to definitize the behavior of ... (parachute)

components under dynamic conditions."

These statements and others like them reflect the con-

sensus that material math models better than those which

have been available will be required before parachute system

computer analyses can become real predictive tools and as a

consequence, make a broader impact on system design and

analysis.

These circuistances led to the start in November 1973

of an in-house program in the Recovery and Crew Station

Branch, Vehicle Equipment Divisio, of the Air Force Flight

Dynamics Laboratory (AFFDL/FER) to develop improved math

models for the dynamic tensile behavior of nylon parachute

materials. The approach taken during this work effort is

discussed in the following section.

(9) Talay, T.A., Parachute Deployment-Parameter Identifica-tion Based on an Analytical Simulation of Viking BLDT AV-4,NASA-TN-D7678, August 1974.

(10) Bobbit, P.J., "Recent Advances and Remaining Voids inParachute Technology," AIAA Aerodynamic Deceleration SystemsTech Committee Position Paper, Astronautics and Aeronautics,October, 1975, pp. 56-63.

6

2. Approach

Since earlier attempts to model the properties of para-

chute materials all seemed to share a theoretical approach

and to have achieved only limited success, the AFFDL/FER pro-

gram was planned to be more empirical in nature. Instead of

assuming some viscoelastic model for the material behavior at

the outset and then struggling to acquire data (elastic and

viscous damping coefficients) to fit, it was intended to

develop the formulation of a realistic model from appropriate

loading data alone. The mathematical expression of the

observed data was to be the goal of the effort, not the

first step.

An experimental phase of the program was planned to

acquire a limited data base for some parachute material of

interest. This was to be followed by an analytical phase to

search for aspects of the data lending themselves to general

mathematical expression over a wide range of load levels and

strain rates; i.e., to develop math models of the data

acquired. Finally, it was planned to code the math models

as computer subroutines for general use in large parachute

analysis computer programs. The material subroutines would

serve to realistically model the dynamic tensile load-strain

behavior of nylon components within the larger computer pro-

gram, be it for parachute system stress analysis, opening

dynamic analysis, stability analysis or design purposes.

After one test case, that is after the successful develop-

ment of one parachute material computer subroutine, it was

further intended to automate the process as much as possible

by writing data processing computer programs to generate

additional material subroutines from new sets of data follow-

ing the general form developed for the test case.

The goal of the program then was to demonstrate the

capability to empirically develop computer subroutines which

could realistically model the tensile behavior of nylon

parachute components. These subroutines would be generated

7

semiautomatically through data processing of limited data

bases acquired for the materials of interest.

3. Scope

The work outlined in the previous section resulted

in two-and-one half man-years of work and involved a nylon

cord and fabric used widely in personnel parachute fabrica-

tion. Only uniaxial tensile behavior of materials was

addressed. The first material selected for modelling was acore-sleeve nylon cord used widely in suspension systems of

personnel parachutes: 400 lb minimum breaking strength,

MIL-C-5040E, Type II, nylon cord.

An apparatus was fabricated to provide dynamic load-

strain data for material samples and was used to acquire data

for load levels up to 300 lb and over a range of strain rates-l

from 1.2 to 6.9 sec .

By early 1975, a computer subroutine modelling the cord

behavior had been demonstrated and was documented in Refer-

ence 11. This cord subroutine was used with encouraging

results in parachute opening dynamics studies conducted in-

house during the same time period as reported in Reference 12.

A second test series was accomplished to acquire data

for uniaxial samples in both the warp and fill directions of a

light ripstop nylon fabric also used extensively in fabrica-

tion of personnel parachutes: l.l-oz per square yard, MIL-C-

7020F, Type I. The warp direction is that of the yarns which

run parallel the length of a bolt of fabric as it is woven.

The fill direction is normal to the warp direction and is that

of the yarns which run back and forth across the bolt of fabric

as it is woven. This time, data was acquired up to rupture

(11) McCarty, R., A Computer Subroutine for the Load-Elongation of Parachute Suspension Lines, AIAA Paper 75-1362,1975.

(12) Keck, E.L., A Computer Simulation of Parachute OpeningDynamics, AIAA Paper 75-1379, 1975.

8

loads and over a range of strain rates from 1.3 to 4.9-1

sec .

Seven small data processing computer programs were

written to automate the generation of material subroutines

as much as possible. These programs were used to derive sub-

routines from both the fabric warp and fill data bases.

The purpose of this report is to document the overall

work effort and publish the nylon material computer sub-

routines developed. It is also to encourage the application

of these subroutines and the development of additional sub-

routines for other parachute materials by means of the

efficient data processing capability now available for their

generation.

9

SECTION II

DATA ACQUISITION

1. Methods

This work effort involved a nylon cord and fabric used

widely in personnel parachute fabrication, and the primary

inhouse application of the computer subroutines developed was

intended to be in simulation of personnel parachute opening

dynamics, as reported in Reference 12. For these reasons, a

test method was sought which would duplicate to a consider-

able extent the dynamic loading environment experienced by

these materials in personnel parachute applications. All

constant strain rate methods were rejected because strain

rates experienced during parachute operation are not con-

stant but rather suffer large excursions and sign changes. A

drop-weight test method was adopted because it provided

periodic variation of strain rate and would allow data

acquisition over the full range of loading and strain rates

(0 to 4.5 sec -1 ) occurring during conventional deployment and

inflation of personnel parachutes.

2. Apparatus

A test fixture was designed and fabricated which would

allow tensile impact loads to be applied to samples of para-

chute materials over a wide range of initial strain rates and

impact energies. Figure 5 illustrates the device. Material

samples were oriented vertically in the fixture, the upper

end being fixed and the lower being attached to a weighted

sled. The main component was a 120-inch high tower fixed

along its length to a concrete block wall. The tower supported

two hard aluminum rails which served to guide the weight sled

(12) Keck, E.L., A Computer Simulation of Parachute OpeningDynamics, AIAA Paper 75-1379, 1975.

10i0

SAMPLE CLOSCILLOGRAPH

SLIED

Figure 5. Schematic for Tensile Impact Test Fixture.

as it moved vertically. The rails engaged the flanges of

four ball bearing wheels, two on either side of the weight

sled. A solenoid-operated device on the tower provided for

release of the drop weight sled from various heights. Com-

binations of drop height and drop weight were selected to

obtain the initial strain rates and impact energies desired

during testing. Rubber bungee cords were used in some tests

to yield sled accelerations exceeding one gravity.

The upper attachment point for material samples was a

strain gage load link used to acquire load history data

during a test. The weighted drop sled had extending downward

from its bottom center a 36-inch-long rod the tip of which

entered a 30-inch Linear Variable Differential Transformer

(LVDT) used to acquire sled displacement data during a test.

Signals from the load link and LVDT were conditioned and

used to drive galvanometers in a direct writing type oscillo-

graph. An automatic test sequencer drove the release

11

mechanism and data acquisition equipment. Data was recorded

for at least three full loading cycles (bounces) on every

test. Figures 6 through 10 show details of the test fixture.

Table 1 contains the list of equipment used in the tensile

impact test fixture.

3. Material Samples

Length of the material samples tested in the tensile

impact fixture were dictated by the range of strain rates

desired in testing. Since the geometry of the test fixture

prevented drop heights exceeding the length of the sample,

the maximum initial strain rate available for (no rubber

bungee) drop tests follows Equation (1). The sample lengths

EDOTmax = [(2g)/LO I1 / 2 (1)

EDOTmax - maximum possible initial strain rate

g - acceleration of gravity

LO - unstressed length of sample

that were selected allowed cord strain rates up to 4.2 sec 1

and fabric strain rates up to 4.9 sec 1 .

Cord samples had the ends doubled back and zig-zagstitched to allow steel pin attachments in the test fixture.

The ends of warp and fill fabric samples were sandwiched

between thin aluminum plates with an epoxy resin. Holes

drilled in these end plates provided the same steel pin

attachment used for the cord samples. Fabric samples were cut

slightly wider than desired, then after epoxying on the end

plates, extra yarn ends were cut from both sides of the

sample to obtain the desired sample width. All fabric samples

had the same number of longitudinal yarn ends. Figures 11 and

12 illustrate the material samples used. In each case, all

samples were cut from the same lot of material. All samples

were tested at temperatures between 66 and 88 degrees

Fahrenheit.

12

4J

4

U)

04

10

.,q

13

41

0

0

0)

4

*e r4

14

7 i i

Figure 8. Tensile Impact Test Fixture.

LOAD

P LINKAbATTA MENT

MECHANISM

4b

Pigue 9 Loa Lik Atachent nd led elese Mchaism

16t

AlbS UD

PRBS KT

vA

Figure 10. Drop Sled Probe in LVDT.

17

TABLE 1

IMPACT TEST FIXTURE COMPONENTS

Component Model Performance

steel strain gage S/N D-l (FER) 0-60 lb or 0-140 lblink, bending

aluminum strain gage S/N 300-1 (FER) 0-300 lblink, tension

Schaevitz LVDT P/N 10000 HR + 10 in displ.

Schaevitz signal P/N SCM 025 (displ. channel)conditioner

SOLA regulated Cat. 80-36-1300power supply

Bell & Howell P/N 8-115-1 (loads channel)

signal conditioner

Honeywell 1508-T13679HK000

Visicorder (oscillograph)

Honeywell M-1000 0-600 Hzgalvanometer (fluid damped) (loads channel)

Honeywell M200-120 0-120 Hzgalvanometer (displ. channel)

18

$404'u

0

to

19o

1.5 in 40.0 in 1.5 in

Cord Sample

-2. 0 in

2.5 in -32.75 in 2.5 inFabric Samples

Figure 12. Test Sample Dimensions.

4. Static Data

The Composites and Fibrous Materials Branch, Non-MetallicMaterials Division of the Air Force Materials Laboratory

(AFML) performed static testing of cord, fabric warp and fillsamples. Tests were performed on an Instron machine at strain

rates of 0.01 sec -1 . Rubber lined pressure grips were used tofix samples; all sample gauge lengths were 20 inches. Thisstatic data served as a baseline from which to measure strain

rate effects in the high strain rate data acquired duringsubsequent dynamic (drop weight) testing. Load-strain plots

made from the reduced AFML data are contained in Appendix A.Static test parameters may be found in Table 2.

5. Creep Data

Creep strain data was acquired for fabric warp and fill

samples by suspending the weight sled from a material sampleon the Tensile Impact Test Fixture. The oscillograph wasused to record the static tensile load and the resulting

20&

strain history exhibited by the material sample. Creep data

was recorded under three different loading conditions. A

sample of reduced creep data is shown in Figure 13. No data

OD 00.0 0Primary Secondary .,*0.0.* 0

creep creep . ow

.000~~0000000C @000°

2 fabric warp sampleW0

o0 15 lb/in static loading

000

0

0

0.0 i.

Time (sec)

Figure 13. Typical Creep Strain Data.

was acquired for the tertiary stage of creep; i.e., no creeptests were conducted which resulted in material failure.

6. Dynamic Data

Each dynamic, or drop weight, test was conducted witha previously unloaded material sample. Cord samples weretested at eleven different combinations of drop weightand drop height, fabric fill samples at nine combinations,and fabric warp samples at nine combinations. Three testswere performed at each test condition for a total of 87 tensile

21

impact tests. Table 2 lists parameters for one test at each

condition. Parameters for those remaining tests not shown on

Table 2 are very similar for any particular test condition, the

differences being due primarily to small variations in the

length of fabricated test samples. Sample length for cord

samples was measured between centers of the steel pins used

to mount the samples in the fixture. Sample length for

fabric samples was measured between edges of the aluminum end

plates as shown in Figure 12. Drop height was defined to be the

distance between the sled release position and the sled

position at the instant the recorded tensile load rose

above zero. Figure 14 shows a typical oscillograph test and

illustrates how the sled position at load rise was determined.

This position was referred to as the sled zero displacement

point and also served as the point from which to measure

material sample strain.

7. Data Reduction

The analog load-time and displacement-time traces on

each oscillograph record were digitized at uniform intervals,

25 increments per loading cycle including values for peak

load and peak displacement. Each data set was checked for

reduction errors and corrected accordingly when any were found.

Since load data and displacement data channels were calibratedonly once at the start of each test series, the following pro-

cedure was devised to measure calibration errors. It was

assumed that no calibration error was present in the oscillograph

timing marks. The load-time data for each drop weight test was

pointwise fit with a natural cubic spline as described in

Reference 13 and numerically integrated twice to calculate

a corresponding sled displacement history. Friction between

(13) DeBoor, C., and Rice, J., Cubic Spline Approximation II-Variable Knots, Computer Science Department TR-21, PurdueUniversity, April 1968.

22

t

TABLE 2TENSILE TEST PARAMETERS

Sample Drop Drop Initial Peak PeakTest Length Height Mass Strain rate Load Strain

Number (ft) (ft) (si) (sec- (ib) (in/in)

lMi a 3.31 0.35 0.052 1.43 17.7 0.0422-2 a 3.23 0.27 0.275 1.29 50.2 0.0793-3 a 3.28 0.32 0.497 1.38 76.8 0.1054-1 a 3.29 1.59 0.052 3.07 40.9 0.0675-3 a 3.28 1.57 0.274 3.07 95.0 0.1316-1 a 3.27 1.60 0.492 3.10 136.7 0.1627-2 a 3.28 2.82 0.052 4.11 53.2 0.0798-2 a 3.28 2.86 0.274 4.13 125.3 0.1659-2 a 3.29 2.87 0.492 4.13 190.0 0.212

10-3 a 3.27 2.85 0.714 4.14 255.4 0.24411-1 a 3.32 0.052 6.88 85.0 0.120*2C a 1.67 - - .01 409.9 0.355*3C a 1.67 - - .01 396.0 0.348iWI b 2.72 0.22 0.943 1.38 46.1** 0.1762Wl b 2.72 0.22 0.501 1.38 25.0** 0.1213W1 b 2.71 0.21 0.167 1.35 10.8** 0.050

*1W4 b 2.70 1.45 0.498 3.58 52.9** 0.201lW5 b 2.71 1.46 0.278 3.58 38.7** 0.1606W3 b 2.70 1.45 0.062 3.57 13.6** 0.0703W7 b 2.69 2.70 0.279 4.89 53.1** 0.2038W2 b 2.70 2.70 0.166 4.88 39.2** 0.1569W2 b 2.70 2.71 0.062 4.88 18.8** 0.101

*16W b 1.67 - - .01 40.9** 0.207*30W b 1.67 - - .01 40.7** 0.209IF3 c 2.72 0.22 0.943 1.39 46.5** 0.2472F3 c 2.72 0.22 0.501 1.40 25.5** 0.1743F2 c 2.70 0.21 0.167 1.35 10.8** 0.0833F4 c 2.71 1.46 0.498 3.58 51.7** 0.2645F2 c 2.72 1.47 0.279 3.57 35.1** 0.2076F2 c 2.71 1.46 0.062 3.58 12.5** 0.099

*3F7 c 2.71 2.71 0.279 4.87 42.6** 0.2358F1 c 2.71 2.71 0.166 4.87 33.7** 0.2119F3 c 2.72 2.72 0.062 4.87 17.0** 0.126

*3F1 c 1.67 - - .01 39.3** 0.257*30F c 1.67 - - .01 40.3** 0.271

*Material rupture occurred. **(lb/in) ***Bungee cord used.

a - cord samples b - warp samples c - fill samples

23

~Sled zero displacement

displacement

tensile load

time

Figure 14. Tensile Impact Test Oscillograph Record.

sled and test fixture guide rails was assumed to be negligible

in the calculation. The sled displacement data computed for

a given test was compared with the sled displacement data

recorded during that test. Figure 15 illustrates the method.

Any difference between recorded and calculated periods of

motion was taken as evidence of calibration error in the

load data, since displacement data calibration error could not

alter the recorded period of motion. Sled displacement

history was then recalculated as a boundary value problem,

assuming various load calibration errors until the one

was found which resulted in agreement between recorded and

calculated periods of motion. Figure 16 illustrates typical

correlation after correction for load calibration error.

Any remaining difference between the two maximum sled

24

t

0 0 0 go0 0*

00

0 recorded

C

E0calculatedfrom recorded0

CL ~ load-time0a)data0

00

0)

00

0)0.0 .05 .110

Time ( sec)

Figure 15. Calibration Error Determination.

090aS recorded

calculated from

O load-time data~ 'A corrected for load

calibration error

C,,

0.0 .05 .10Time (sec)

Figure 16. Load Calibration Error Correction.

25

displacements was attributed to calibration error in the

displacement data. That displacement data calibration error

which resulted in agreement between calculated and recorded

maximum displacements was determined. Figure 17 shows typical

correlation between the two sled displacement histories

after correcting the data for those calibration errors

implied by the method just described. The excellent agree-

ment between shapes of the two displacement histories is

0recorded datacorrected for

" displacementE calibration

a, a

ero

U calculated fromload-timTe datecorrected for load

0 calibration error

a,

0.0 .d5 .AOTime (sec)

Figure 17. Displacement Calibration Error Correction.

taken as evidence that nonlinearities in transducers and

recording equipment, friction in the tensile impact test

fixture, and other random sources of recording and reduction

errors were negligible for the purposes of this study.

Table 3 lists calibration errors derived for those tests in

Table 2. Load-strain and load-time plots of corrected

data for these tests are contained in Appendix A.

265

TABLE 3LOAD AND DISPLACEMENT DATA CALIBRATION ERRORS ASSUMED

Test Percent Load Percent DisplacementNumber Cal. Error Cal. ErrorIml 3.0 7.02-2 1.0 4.0

3-3 6.0 5.0

4-1 0.0 6.0

5-3 5.0 5.06-1 -1.0 3.0

7-2 -2.0 7.08-2 -1.0 6.0

9-2 -1.0 4.0

10-3 -1.0 3.011-1 -2.0 0.0

1Wi 4.0 -6.02W. -2.0 -4.0

3W1 -2.0 -4.0IW4 2.0 -7.0IW5 3.0 -1.0

6W3 -3.0 1.0

3W7 4.0 0.08W2 5.0 -2.0

9W2 -1.0 -2.0

1F3 4.0 -7.0

2F3 -1.6 -5.3

3F2 -1.6 -5.3

3F4 4.0 -3.05F2 7.0 3.0

6F2 -5.0 -4.03F7 4.6 -1.3

8F1 6.0 5.09F3 -1.6 -1.3

27

SECTION III

DATA ANALYSIS

1. Method

In developing math models from the data bases acquired,

an attempt was made to isolate individual aspects of the

material behavior. It was hoped that each of these features

could be modelled independently and then that all could be

combined to express the observed net behavior. Candidate

features for doing this were drawn from the list discussed

in Section I.l: nonlinear loading characteristic, strain-

rate sensitivity, hysteresis, plasticity, and creep. The

first feature selected for modelling was creep. This is

discussed in the following section.

2. Creep

The data which was acquired for creep is shown in

Figure 18. It exhibits classic primary and secondary creep

.oo

o 0 00 0 00 0 00 0

0 o0~ fill 1 15.4 lb/in

C

_ warp 14 .7 lb/in 00S. 0000 00 00 00 00 00 0 00800 0a0a 0 00 000 000

.5 0 0000 fill 8.4 b/in

warp 8.0 lb/in

0 0 0 0 0 0 0 00 0 00 00 0 0 0 0 0 0 0 0

fill 1.0 lbin0 0 0 00 0 0 00 a00 0 000 00 a0 0 00 00 000 0a0 a0 00a

0.0 1.5 3.0

Time (sec)

Figure 18. Creep Strain Histories for Fabric.

28i

as defined in References 14 and 15. A great deal of similarity

appears in all the creep data shown, aside from the fact thatthe initial strains under load differ widely. Little measur-able creep resulted at very low loads (1 lb/in) on fill testsamples. Nearly doubling the loading in the case of bothwarp and fill samples had little effect on the shape of theresulting strain-time curve. Similarily, no significantdifference in curve shape can be seen between warp and filldata taken at about the same level of loading. Transitionfrom primary to secondary creep occurs at about 1.8 seconds inall cases. Based on these observations and on the verylimited data base acquired, a simple creep model was developedwhich proved sufficient for the purpose at hand and whichthrew a new light on the mechanism underlying the strain ratesensitivity of nylon. This latter result will be discussedmore fully in Section 111.3.

The creep model adopted assumes that creep behavior isindependent of the construction of the particular componentfabricated from nylon be it fabric, cord, webbing, etc. Itfurther assumes no effects of material temperature. The modeldoes assume that primary creep occurs from 0.0 to 1.8 secondsunder any loading, and secondary creep from 1.8 secondsforward in time. Tertiary creep to material rupture is notmodelled. The effect of this omission is discussed in the

next section. Identical creep strain histories are assumedfor all loadings above 20 percent of the minimum breakingstrength for the material; i.e., at loadings above 20 percentof material breaking strength, creep ceases to be a functionof static load and time and becomes a function of time alone.

(14) Crandall, S.H., and Dahl, N.C., An Introduction to theMechanics of Solids, McGraw-Hill, 1959, pp 222-223.

(51) Bruhn, E.F., Analysis and Design of Flight VehicleStructures, Tri-State Offset, 1965, pp. BI.12-Bl.13.

29

For load levels between 0 and 20 percent breaking strength,

the creep strain history is linearly scaled between zero and

that creep strain history assumed for higher load levels.

The model is extrapolated indefinitely in both independent

variables: load and time. Figure 19 illustrates this model.

C

C

Cn

74-

• " e (sec)

0 / // . / I

/ /

Figure 19. Creep Strain Model.

Values for initial strain (at t = 0) have been subtracted out

from the data in Figure 19. This surface representing strain

as a function of load and time was differentiated with

respect to time to yield a second surface representing creep

strain rate as discussed further in Reference 16. Figure 20

shows this surface. Double linear interpolation on the

second surface for a given load and time gives a correspond-

ing creep strain rate. For the case of dynamic loading, a

(16) Polakowski, N.H., and Ripling, E.J., Strength andStructure of Engineering Materials, Prentice-Hall, 1966p. 429.

30

) -

/ C/

¢ I\

/ I, I 4.-

/I I

I i i

Figure 20. Creep Strain Rate Model.

series of creep strain rates can be determined which corre-

spond to any given load-time path as shown in Figure 21.

Integration along the creep strain rate path shown in

Figure 21 yields instantaneous creep strain for the given

loading history. This is the form in which the nylon creep

model was adopted. Tabular data is used to represent the

surface shown in Figures 20 and 21. Double linear inter-

polation and integration of the interpolated values is

performed along the load-time path experienced by the

material. The corresponding creep strain history is the

result.

This creep model is probably more sound for secondary

creep than for primary creep as a result of the test method

used. The ideal creep strain test would provide for the

instantaneous application of a static load and subsequent

recording of strain-time data as shown in Figure 22. In

practice, tensile loads were not applied instantaneously.

31

/ I' a'

/ I '\ 0 f

/ I

/r

, ' I ,'5 - . rate path/e

i 2 reep Hstr

/ I "As aru/ / o t p , d was

, ",f/ /'7"]1--

/-I- ' " - P th / /

( I /

Figure 21. Creep Strain Rate History.

As a result, the early portion of the primary creep data was

lost. Figure 23 illustrates that the effect of this would

be to record values for primary creep strain rates which were

too low. This concern was substantiated later in the

analysis and will be discussed in greater detail in Section

111.4. Data for secondary creep strain and strain rate

remained unaffected by this technique-related problem.

3. Loading Characteristic

It was apparent from the data acquired that consideration

of two behavioral aspects of nylon would be required in order

to model the loading characteristic of the material. These

were the nonlinearity of the loading characteristic and its

sensitivity to strain rate. Figure 24 illustrates some

dynamic and static loading characteristics from the fabric

fill data. The nonlinearity is apparent and the dynamic

behavior is considerably stiffer in every case. This latter

fact plus the experience that had been gained in modelling

32

t i.. lI~ l I I I '

m actual initial

straisran rate.....oi secondarya

pprimary

0 Time

VI

0iTimem

Figure 22. Ideal Creep Test.

measured initial

o secondaryU) primary

0 Time

E 0

0 Time

Figure 23. Actual Creep Test.

33

creep suggested that all or a part of the strain-rate

sensitivity of nylon might simply be a manifestation ofmaterial creep. To test this hypothesis, the following steps

were taken. The load-time histories for all tests (includingstatic) of a material were input to the creep model shown in

Figure 21 and described in the last section. The resulting

creep strain rate history for each test was integrated toyield a corresponding creep strain history. This creep

history was subtracted out from the loading characteristic

for each test, making it stiffer in every case. Figure 25

illustrates this for a static test. The computed creep

strain contribution for dynamic tests was much less signifi-

cant than that illustrated for the static case. This

result was to be expected since creep is time dependent and

time under load was two orders of magnitude higher for

to dynamic

data

"-staticdata

n -I

0

00.0 0.15 o.3o

Strain (in/in)

Figure 24. Fabric Fill Loading Characteristics.

34

Test 3FI

static characteristic with creep p|~ effects subtracted out -'

S/ ---- recorded staticcharacteristic

,'.,

00

0.0 .12 .24Strain (in/in)

Figure 25. Creep Contribution to Total Strain.

static than for dynamic tests. The result of this exerciseis shown in Figure 26. This is a plot of the same fabricfill loading characteristics shown in Figure 24 but forwhich the effects of creep have been subtracted out. Thedispersion customarily associated with the strain ratesensitivity of nylon is no longer evident as in Figure 24.The only data lying outside the narrow band is that nearmaterial rupture from the static tests. Had the tertiarystage of creep been included in the creep model, much largercreep strains would have been computed in the vicinity ofstatic rupture and these data points would have been movedcloser to the narrow band of data.

Figure 26 implies that it is reasonable to think interms of a strain rate independent loading characteristicfor nylon. This thinking was followed in modelling loadingcharacteristics. The data was least squares fit with asix-knot natural cubic spline which preserved the non-linearity of the data. The coupling of the previously

35

00

strain rate independent 00loading characteristic 0 .It

0- 0

.00t00

W x- rupture_J00

00 0

0 o,00 0o

0.0 A1 3Strain (in/in)

Figure 26. Loading Characteristics With Creep Effects Subtracted Out.

described creep model to this cubic spline fit then com-

pleted the definition of the loading characteristic. The

spline fit provided the nonlinear strain rate independent

behavior required while the creep model provided the

necessary strain rate sensitivity. It should be emphasized

that loading characteristics discussed thus far have been

for initial loading of previously unloaded samples only.Subsequent or repeated loading behavior is treated in later

sections.

4. Plasticity

With the development of the creep and loading character-

istic models just described it became possible to simulate

accurately all of the data acquired (static and dynamic) for

initial loading of material samples up to the point of maxi-mum strain. Attention turned next to behavior beyond this

point, in particular to the plastic strain resulting from

this initial loading. At this point in its development, the

36

model predicted only a slight plastic strain at the beginning

of the second loading cycle. This was a creep effect alone

and is indicated as such in Figure 27. The difference

between the smaller plastic strain predicted by the model

with creep and the larger plastic strain observed in the

data was defined as the residual strain, ELR, for modelling

purposes. Dynamic tests were simulated using the current

version of the model to generate plots similar to Figure 27,

and values for residual strain were measured from these

plots and tabulated. It was readily apparent from this that

residual strain, ELR, increased with maximum strain, ELM.

A plot of residual strain versus maximum strain shown in

Figure 28 revealed a nearly cubic dependence so the data was

fit with a cubic polynomial.

Having derived a simple expression for residual strain

as a function of maximum strain, it remained to use this

expression to correctly model subsequent or repeated loading

characteristics for the material. It was observed that the

slope of the recorded loading characteristic increased after

each loading cycle and "pointed toward" a common vertex at

the current maximum strain. This is illustrated in Figure 29.

Other investigations, such as in Reference 17, have noted

these same aspects of repeated loading behavior. This

suggested that the expression derived for residual strain

might be used to transform the expression for the loading

characteristic. The transformation would be a linear one

judging from the appearance of geometric similarity between

first, second, and third loading characteristics. It would

provide that the origin of the loading characteristic move

from zero strain for the first loading cycle to the value of

the current plastic strain for the second loading cycle and

(17) Groom, J.J., Investigation of a Simple Dynamic Systemwith a Woven-Nylon Taee Member Displan i Nonlinear Daming,Thesis for Master of Science, Ohio State University,

1974,

pp. 51-54.

37

IA maximum strain

Test 5F2

CL

dahs moe wt

.0 4

Fiur 27 Mode Wit CrepEfet

0-I

0 data

00

0 dat 0

0 1 T

0.0 .4.28ELM (in/in)

Figure 28. Residual Strain as a Function of Maximum Strain.

38

maximumrO. strain

Test 2F3

.0~ItI

o plastic strain 0.10 0.20

Strain (in/in)

Figure 29. Repeated Loading Characteristics.

that all subsequent characteristics still pass through the

point of maximum strain. The variable ELOT defined by

Equation (2) was intended to meet all these requirements.

Whenever material strain, ELO, is equal to the current

residual strain, ELR, the value of ELOT becomes zero. When

ELO is equal to the current maximum strain, ELM, the value

of ELOT becomes ELM.

ELOT = (ELO - ELR)ELM/(ELM-ELR) (2)

ELO - current material strain

ELR - current material residual strain

ELM - current material maximum strain

ELOT - transform of ELO, this provides for

movement of the loading characteristic

origin along the strain axis as a function

of residual strain ELR.

39

After this definition of ELOT it became possible to use the

cubic spline fit for the loading characteristic (Section

111.3) to model both initial and repeated loading by substi-

tuting either ELO or ELOT as the independent variable as

illustrated in Figure 30. The choice between the two was made

by comparing instantaneous values of ELO and ELM during the

loading history according to Equation (3). During initial

loading, Equation (3-a) describes the loading because at any

given time ELO equals ELM. During subsequent loading to

FT = f(ELO) if ELO = ELM (3-a)

FT = f(ELOT) if ELO < ELM (3-b)

FT - tensile load

ELM - current maximum strain

ELO - current strain

ELOT - transform of ELO

f - cubic spline function

strains less than the maximum strain attained during the

initial loading, Equation (3-b) describes the behavior because

ELO always remains less than ELM. During subsequent loading

which exceeds all previous maximum strains, the behavior again

reverts to Equation (3-a) since ELO equals ELM again. Figure

31 illustrates the behavior of the model at this point with

creep and plasticity effects accounted for. The shift between

first and second loading characteristics is due to both

effects, the shift between second and third is due to the

creep effect alone. All three loading characteristics are

well simulated by the model. It should be noted that, as

suspected (Section 111.2), the level of primary creep originally

modelled was too low by a factor of three or four and had

to be increased to yield the level of correlation illustrated

in Figure 31.

One case remained for which this version of the math

mudel failed to model loading behavior satisfactorily. That

was the case for which the tensile load never returned to

40

EC =f (oad, time)

loading characteristic,-~as a function of ELO

a -09 Loading characteristic_j as a function of ELOT

1 EC-EL-R-H- 0.1l0 strain 0. Oi/n)ELM

0 .0 0.10 ELO (in/in) 0.20

0.0 0.10 ELOT( in/in) 0 .20

Figure 30. Initial and Subsequent Loading.

0-

Test 5F2dashes - model with creep

and plasticityline - dynamic test data

0

0-J

0.0 .14.2Strain (in/in)

Figure 31. Model with Creep and Plasticity Effects.

41

zero after initial loading as shown in Figure 32. Estimation

of residual strain as a function of maximum strain for such

continuously loaded samples showed the same cubic dependence

as that shown in Figure 28 for samples which periodically

experienced zero load. But for the continuously loaded

samples, the observed residual strain was always greater for

the same level of maximum strain. This difference was

attributed to the fact that for samples periodically seeing

zero load the accumulated residual strain had time to relax

while for continuously loaded sample no relaxation could

occur (Section 1.1). This behavior was modelled by using

two curve fits like the one shown in Figure 28, one serving

as an upper bound and one as a lower bound to residual strain.

0maximum strain /

Test IF3 dashes -model withcreep and ,/ ,'

residual/ i

-. strain line - data /' //

A

00.0 .14EC ELR ELM .28

Strain (in/in)

Figure 32. Continuous Loading Characteristics.

Accumulative time under zero load was tracked and used to

interpolate linearly between the two. An example is

illustrated in Figure 33. Immediately upon unloading from a

maximum strain of 0.10 in/in the material exhibits the large

42

material. underload

LU material underzero load

0.0 0.10ELM (in/in)

Figure 33. Residual Strain for Material under Load and underZero Load.

plastic strain A. With the passage of time under zero load,

the plastic strain relaxes or grows less following the pathindicated from A to B. After sufficient time passes, theplastic strain ceases to relax further, permanently assuming

the value represented by B. Data for both curves shown inFigure 33 and for related relaxation times were extracted from

the test data, then this refinement was added to the plasticityportion of the model. At this point, all static and dynamic,

initial and repeated loading characteristics could be

simulated satisfactorily by the model. The only featuremissing was realistic unloading behavior; the strong

hysteresis observed in the data had not yet been accountedfor. The development of this feature of the model is

discussed in the following section.

43

5. Hysteresis

The first observation made regarding unloading behavior

was the apparent geometric similarity among all unloading

characteristics. This similarity has been noted by other

authors, for example Reference 17, and led to the following

approach to modelling unloading.

To provide a common denominator by which to describe

unloading a normalized strain parameter, ELS, was defined

having the form of Equation (4).

ELS = (ELM - ELO)/(ELM - ELR) (4)

ELM - current max.mum strain

ELO - current strain

ELR - current residual strain

ELS - normalized strain

When material strain is maximum, i.e., when ELO equals ELM,

the value of ELS is zero. When the material has unloaded to

its current plastic strain, i.e., when ELO equals ELR, ELS

assumes the value of 1. Figure 34 shows that every unloading

action then, no matter from what maximum strain or to

what plastic strain, involves the variable ELS assuming

values over the range of 0 to 1. To further specify

unloading, the variable FD, as illustrated in Figure 34 was

defined to be the difference between that load predicted by

the current version of the model and that load observed in

the data at a given strain during material unloading. Plots

similar to Figure 34 were generated for all data on hand withthe model results being linearly scaled such that computed

and experimental peak load and strain would coincide exactly.

From these plots tables of FD as a function of ELS were

developed in an attempt to quantify unloading behavior.

Plots of FD versus ELS for various tests are shown in

Figure 35. The shape of the plots showed general similarity

(17) Groom, J.J., Investigation of a Simple Dynamic Systemwith a Woven-Nylon Tape Member Displaying Nonlinear Damping,Thesis for Master of Science, Ohio State University, 1974.

44

Test 5F2dashes-model with creep

-~~ and plasticity I

line -dynamic test ,

data - .

o -0J

_j/

0/

0

1.0 Test 0.0

0

0

0.0 0.5 1.0ELS

Figure 35. FD versus ELS Data.

45

for all tests but the magnitudes varied over a very wide

range. It was observed, however, that the magnitudes varied

directly with the maximum strain experienced by the material

during the test. To determine the form of this dependence,

the following steps were taken. One of the FD versus ELS

curves for the material was selected arbitrarily and inte-

grated in order to determine the area beneath the curve. All

other FD versus ELS curves for the same meterial were

multiplied by a ratio with a value such that the area under

each became equal to the arbitrarily chosen reference area.

The resulting group of data points was fit with a cubic

spline as shown in Figure 36. This fit was forced to pass

through zero at ELS = 0.0 and ELS = 1.0. The ratios requiredto equate areas in this manner were found to be a simple

function of maximum strain as shown in Figure 37 and wereleast squares fit with a cubic polynomial.

00j" 0 0

0°0 - - -- .°

0 N 00 0 0

1 0 0 0

0'" 0 0

0: a

% '-----cubic spline 0

< b - / ,fit0 0/

I , oI a

fabric fill data 0 .1\ o

00

0.0 0.5 1.0ELS

Figure 36. Ratioed FD versus ELS Data.

46

/'

fabric fill data

cubic polynomial

0

00

0.0 0.10 0.20ELMI (in/in)

Figure 37. FD Ratios as a Function of ELM1.

The analysis just described provided a simple and

general definition of unloading. The form of the expression

is shown in Equation (5). It implies that three pieces of

information are required in order to calculate FD: Thevalu ofFD

value of FR which is a function of normalized strainRATIO

FD - FD RATIO (ELM - ELR) when EDOT < 0 (5)

RARATIATI (ELM -ELR)

= 0 when EDOT > 0

FDRATIO - six knot least squares fit cubic spline (Figure 36)

RATIO - least squares fit cubic polynomial (Figure 37)

(ELS), the value of RATIO which is a function of maximum

strain (ELMl), and the value of ELM (and ELR which is a func-

tion of ELM per Figure 28). The value of FD is determined7RATIO

47

from the curve fit illustrated in Figure 36, and the value

of RATIO is determined from the curve fit illustrated in

Figure 37. ELS, ELM1, ELM and ELR are continuously cal-

culated by the material model. Equation (5) also implies

that the value of FD is zero whenever material strain rate

is positive. When the material is loading, no FD contribu-

tion is felt by the model. But, whenever the material is

unloading, a positive value of FD is calculated and sub-

tracted from the current load.

The approach just outlined served very well to model all

drop weight test data which periodically experienced zero

load. This is illustrated in Figure 38. It should be noted

that the third term in Equation (5) was added to properly

scale FD for subsequent or repeated loading cycles. In this

way, for example, FD loads for the third loading cycle

shown in Figure 38 are scaled for the maximum strain experi-

enced during that loading cycle instead of for the overall

Test 9F3Dots - Full Model

c N Line - Dynamic TestData

0

PjO

00.0 0.08 0.16

Strain (in/in)

Figure 38. Model with Creep, Plasticity, and Hysteresis Effects.

48

maximum strain which had occurred earlier in the first

loading cycle.

This description of material unloading failed for one

class of drop weight tests, however, that being those tests

during which the material sample was continuously loaded;

i.e., those tests for which the drop weight sled did not

bounce. Figure 39 shows that since unloading was modelled

by subtracting an appropriate load component only when the

material strain rate was negative, a force discontinuity was

generated by the model whenever the strain rate changed from

negative to positive at nonzero values of tensile load. This

undesirable feature of the model was overcome by arbitrarily

adding a strain rate term to the overall expression for FD.

This term is only active when negative strain rates are

decreasing, i.e., when material strain rates are negative

and acceleration of sample end points is positive. The rate

term is a ratio of current negative strain rate to maximum

0to)

Test IF3Simulation I

/ I

6. . I/ I,

0

0.0 0.14 0.28Strain (in/in)

Figure 39. Model Unloading Discontinuity.

49

negative strain rate during the current unloading cycle. It

is used to drive FD to zero as the current material negative

strain rate approaches zero as shown in Figure 40. Load

histories resulting from this approach still had discontinuous

first and second derivatives with time.

At this point in its development, the model included all

the major features of material behavior outlined in Section

I.l. It provided the strong nonlinearity characteristic of

nylon, the sensitivity to strain rate, significant hysteresis,large plastic strains, and cre fc -1 -hhemode1ad not

been used--to-simu-I-te load-time or strain-time behavior ofthe material, however, When force-time correlation was first

studied, room for improvement became apparent. The next

section deals with this final stage of model development.

6. Damping

As discussed in Section I.1, the area included within aload-strain diagram for one loading/unloading cycle of the

0-

Test 2F3Dashes - full modelLine dynamic test

data

'U

0

00.0 0.10 0.20

Strain (in/in)

Figure 40. Model with Continuous Loading Term.

50

.. .•,&

material represents the kinetic energy dissipated during

that cycle. The magnitude of this energy dissipation

determines among other things the resulting unforced period

of motion or free damped natural frequency for simple mass-

material systems. In view of this, the following approach

was taken to optimize load-time correlation. A multiplicative

constant VSFD was added to the expression for FD alreadydescribed in Equation (5). For each data set a value of

VSFD was determined which resulted in the best load-time

correlation. It became apparent from doing this that

.reater--vaue of VSFD were required for those tests per-formed at higher strain rates. A graph of VSFD versus strain

rate as shown in Figure 41 revealed a linear dependence,

the first and only evidence of linear viscous damping

encountered during data analysis.

A linear fit was made to the VSFD data and was added as

an additional term to the steadily growing expression for FD

as shown by Equation (6).

-- 0 Test 2-2o Test 3-30 Test 4-111 Test 5- 3 1 0

0U_ 0C,,> / Test 7-2

* Test 8-2i Test 9-2A Test 10-3

0,6 1.0 .0 5.0

Strain Rate (sec")

Figure 41. VSFD versus Strain Rate.

51

FD = FD RATIO(ELMl - ELR) VSFD when EDOT < 0 (6)RATIO (ELM - ELR)

= 0 when EDOT > 0

FDRAO - see Equation (5)RATIO

RATIO - see Equation (5)

VSFD - linear viscous damping term

The first and second terms have already been discussed in

Equation (5). The third term is that discussed in Section

111.5 to scale FD for repeated loading cycles, and the fourth

term is the linear viscous damping term just described.

This final expression for FD improved the load-time or

phase correlation obtained to a satisfactory level as shown

in Figure 42. Development of math models for the dynamic

loading of nylon parachute materials was not carried beyond

this point.

0Test 2F3Dashes - full modelLine- dynamic test data

C

-o

0

0

0 __ _ _ _ _____ __ _ __ _ __ _

0.0 0.4 0.8Time (sec)

Figure 42. Typical Model-Data Phase Correlation.

52

SECTION IV

COMPUTER SUBROUTINES

1. Data Processing

As already discussed in Section 1.2, one of the goals of

this work effort was to develop the capability through auto-

matic data processing computer programs to generate additional

models for a variety of parachute materials as the needs arose.

To this end, and after obtaining satisfactory results with the

manual development of one model as a test case, as documented

in Reference ii, several plotting and data processing computer

programs were written. Each of these was intended to automate

as much as possible one of the data manipulation and fitting

processes discussed in Section III. The flow chart in Figure

43 illustrates the following discussion. Each box in the

figure represents a data processing computer program. The

section in this report which discusses the analysis performed

by each program is included in parenthesis in the same box.

The following is a brief description of each program in the

order in which they are executed during data processing:

1. Program OKDATA reads raw load, displacement, and time

data acquired from drop weight testing. Reduction errors are

also read and are used to correct the data accordingly. Cor-

rected force-time data is pointwise fit with a cubic spline

and integrated twice to calculate corresponding displacement-

time data. Experimental and calculated displacement-time

data are overplotted for visual correlation as shown in Figure

15. Subsequent runs of OKDATA are used to determine values

for displacement and load data calibration errors following

Figure 16 and 17 and to correct the data accordingly for

these.

(11) McCarty, R.E., A Computer Subroutine for the Load-ElongationCharacteristics of Parachute Suspension Lines, AIAA paper75-1362, 1975.

53

RAW CREEP DATA RAW DROP-WEIGHT DATA

PROGRAM CREEP jPROGRAM OKDATA(SECTION 111.2) (SECTION 11.7)

CREEP MODEL(FIG. 20)

f PROGRAM EXTEND L CORRECTED DROP-WEIGHT

(SECTION 111.3) TEST DATA (FIG'S 15-17)INITIAL LOADING

MODEL (FIG. 26)

P ELR VS ELM DATA

(SECTION 111.41 (SECTION 111.4)

THIRD ORDER POLYNOMIALFIT FOR ELR VS ELM (FIG. 28)

REPEATED LOADINGMODEL (FIG. 30)

PRGA BUC (FIG'S 3435 POGA

(SECTION 111. 5) LHYSTER]

UAI NG MOEI G'S 36, 37) PROGRAM MADLOT

FULL SUBROUTINE MODEL FOR SUBROUTINE MODEL

PARACHUTE MATERIAL (APP. B) OR MATERIAL

! ~ PLOTS OF CORRELATION

BETWEEN DATA ANDSUBROUTINE MODELRESULTS (APP. A)

Figure 43. Data Processing Flow Diagram.

54

£'

2. Program CREEP is designed to smooth and differentiate

creep strain data (strain versus time). Tabular data is gen-

erated for a surface such as that illustrated in Figure 20 as

a function of load and time.

3. Program EXTEND requires two types of input, the first

being the creep strain rate table generated by program CREEPand the second being corrected load, strain, and time data

generated by program OKDATA. Data for all initial loading

characteristics are isolated. Creep effects are calculated for

each loading history and subtracted out from the correspondingloading characteristic. Finally, all altered loading character-

istics are overplotted and least squares fit with a cubic

spline as illustrated in Figure 26. The two arrays and one

matrix required to define the spline fit are printed out.

4. Program BOUNCE is a Control Data Corporation 777 Inter-

active Graphics System program, per Reference 18, which allowsthe interactive determination of residual strain from plots

similar to Figure 27. Tabular data for residual strain as afunction of maximum strain is output for all data sets

processed.

5. Program POLYFIT reads residual strain tabular data

generated by program BOUNCE and fits it with a third order

polynomial constrained to pass. through the origin as shown in

Figure 28.

6. Program BOUNCE also serves to generate plots similar

to Figure 34. Tabular data for FD as a function of the

normalized strain parameter, ELS, are generated.

7. Program HYSTER reads the FD versus ELS tabular data

generated by program BOUNCE. It performs the analysis dis-

cussed in Section 111.5 required to generate plots like

Figures 36 and 37. Coefficient arrays for the FD cubic spline

fit and the RATIO polynomial fit are printed.

(18) 777 Interactive Graphics System, Version 2.1, ReferenceManual, Control Data Corporation publication number 17321800,e-vion B, 30 October 1975.

55

8. Program MADLOT (Mathematical Analog for the Dynamic

Loading of Textiles) incorporates the finished material model

as a subroutine. It simulates the dynamics of the drop weight

test apparatus used for this work and overplots computed and

experimental results. Either static or dynamic data may be

simulated. All plots in Appendix A were generated using

program MADLOT in conjunction with the appropriate material

subroutine.

2. Subroutine Models

The three subroutine models developed with the aid of the

seven data processing programs described in Section IV.l are

listed in Appendix B. The first is a model for 400 lb

strength nylon parachute cord, the second for 1.1 oz nylon

rip stop parachute fabric warp, and the third for 1.1 oz

nylon rip stop parachute fabric fill. Data in them which was

derived directly from execution of the seven data processing

programs is labeled as such at the beginning of each sub-

routine model. Two external functions and one interpolation

routine required by the subroutine models are listed at the

end of Appendix B. The subroutine models are written in

FORTRAN Extended Version 4, per Reference 19. All variable

names used in the subroutine models are defined in the list

of symbols at the beginning of this report.

The parameters involved in calling the subroutine models

from other FORTRAN programs or subroutines are T, Y, and P as

indicated in the listings. T is a scalar quantity which repre-

sents current time in seconds. Y is a vector quantity of

dimension three. Y(l) is the component of relative velocity

in ft/sec of the two end points of a tensile member taken in

the direction parallel the member. A positive value implies

that the ends are moving away from each other. Y(2) is the

(19) FORTRAN Extended, Version 4, Reference Manual, ControlData Corporation publication number 60305600, Revision J,5 March 1976.

56

£7_

current tensile member length in ft. Y(3) is the current

creep strain in the tensile member measured in in/in. The

vector Y carries input data to the subroutine models. P is

also a vector quantity of dimension three. It carries out-

put data from the subroutine models to an integration routine

(a fourth order Runge Kutta routine is used in MADLOT). P(l)

is the component of relative acceleration in ft/sec2 of the

two end points of a tensile member taken in the direction par-

allel to the member. It serves as the integrand in computing

a new value of Y(l). P(2) is the same as Y(l). It serves as

the integrand in computing a new value of Y(2). P(3) is the

current material creep strain rate measured in sec -1 . It

serves as the integrand in computing a new value of Y(3).

The two variables of primary interest in applications of

the subroutine models are EL and FTR. EL represents current

strain in in/in of the tensile member based on the original

unstressed length. FTR represents the current tensile load in

lb for cords (tapes, webs) and in lb/in for fabrics. Values

for both variables are carried from the subroutine models

through the labeled common block named INFO.

Since the subroutine models were used to simulate only

single degree of freedom systems for the purposes of this

report, the dimensions of all load and strain variables is

one. To apply these subroutine models to systems involving

many tensile structural elements will require modification.

For example, for a system of N tensile elements the arrays Y

and P might be dimensioned Y(N,3) and P(N,3) and do-loops

added accordingly.

The following values should be preset prior to calling

the subroutine models for the first time from a main program:

KRL = 1.0 ELM1 = 0.0

KCR = 1.0 EC = 0.0

KDP = 1.0 TF = 0.0

RMAXD2 = I.E-6 TS = 0.0

ELM = 0.0 DELOMAX = 0.0

57

They are carried to the subroutine model through the labeled

common block named INFO.

It is the intent of this report to publish the subroutine

models in a rough format, leaving additional modifications of

a more general nature to be accomplished through a variety of

future applications.

All data included in the subroutine models follows theBritish Engineering system of units. Time is measured in

seconds, load in pounds force, and mass in slugs.

It should be noted that material rupture is not modelledin any manner by the subroutine models. 'Instead, print flags

are set for the two variables ELO and ELOT, the current strainand the transformed strain. Valid ranges for these variables

are defined for each subroutine model. When the valid rangesare exceeded a printed message results. After printed

messages occur, the models continue to function, but with

potentially meaningless results. For some applications, itmay be desirable to modify the subroutine models such that the

tensile load is set to zero above a critical strain in anattempt to simulate rupture.

; 58

SECTION V

RESULTS

Appendix A contains plots to illustrate the correlation

obtained between subroutine models and all static and dynamic

experimental data acquired. Plots are grouped by material

type in the order of cord, warp, and fill. The materials are

more specifically identified in Section 1.3. Within each

grouping dynamic data is presented first, then static. For

each test a load-strain plot is presented first, then a load-

time plot. Material rupture occurred on all static tests and

on the higher energy dynamic tests. Test number and material

strain rate are printed on each plot. For dynamic tests, the

material strain rate indicated is the initial strain rate

occurring at time zero. More specific parameters for each

test are listed in Table 2.

Review of Appendix A reveals that the shape of simulated

initial loading characteristics is quite good for the dynamic

case in general, but somewhat worse for the static case. This

is believed to be primarily due to coarseness in the creep

model, the effects of which become significant only for the

static case. Peak loads and strains calculated for dynamic

tests vary less than 5 percent from the data in most cases,

never more than 10 percent.

The shapes of the initial unloading characteristics are

also accurate although the level or magnitude of the

hysteresis is occasionally low or high as for tests 2F3 and

8FI respectively. The effect of this error is reflected in

the load-time plots for the same tests. Too little damping

occurs during first cycle simulation for test 2F3 while too

much occurs for test 8F1.

Load-strain correlation for second and third loading

cycles varies from quite accurate to only moderately so. Test

8F1 results offer a worst case example. The primary short-

coming of the models seem to be the inability to predict

correct slopes for second and third loading cycles. Slopes

are satisfactory for tests which involve continuous loading

59

such as 1F3 and 2F3, but not so for tests during which the

loads periodically return to zero such as 8F1. The simple

rules adopted to model repeated loading characteristics

(Section III.4) apparently do not provide the capability to

model all loading characteristics very accurately.

A second unsatisfactory feature related to repeated loading

is apparent from the warp test plots in particular. This

is the fact that in addition to the slopes of second and third

loading characteristics being awry, the predicted shape also

is unrealistic. This is due to the fact that warp samples

exhibited a characteristic 'hump' in the initial loading

characteristic. Previously loaded warp samples failed to

redisplay this hump. In dynamic warp test cases, the first

loading characteristic always showed the hump while second

and third ones did not. The subroutine models, however,

represent repeated loading and unloading characteristics by

linearly transforming the initial loading characteristics as

discussed in Section III. This approach preserves the humped

shape of initial loading and reproduces it in all subsequent

loading characteristics. Again, it would appear that the

approach taken to model subsequent loading characteristics

by applying linear transformations to the initial character-

istic (Section III.4) may be overly simplistic.

The slight shift to higher strain between second and

third loading characteristics is modelled very accurately in

every case. This is an effect of material creep alone and

reflects the accuracy with which primary creep has been

modelled.

The level of damping predicted by the models is very

realistic. The envelope of peak loads on load-time plots

calculated by the models agrees closely with that seen in the

data in every case.

In the case of dynamic loading, the material models do

very well in predicting the shape of the loading character-

istic at or near material rupture. Tests 3F4 and 3W7 provide

examples of this respectively.

60

For static rupture, however, the modej performance is

poorer as can be seen for test STAT3OF. This is due to the

fact that tertiary creep effects become significant near

static rupture and that the tertiary stage of creep has not

been included in any of the subroutine models (Section 111.2

and 111.3). In contrast, for dynamic rupture the times to

material failures are so short that creep plays virtually no

part at all in the simulation.

61

SECTION VI

CONCLUSIONS

An empirical approach to modelling the dynamic tensile

behavior of nylon parachute materials is warranted. The

capability of subroutine models of nylon material to simulate

free oscillation data over very broad ranges of strain rate

(nearly three decades) and tensile load has been demon-

strated. This capability is unique and will contribute

significantly to the improvement of parachute recovery

system dynamic analyses.

The strain rate sensitivity so characteristic of nylonmaterials may be modelled accurately by coupling a strain

rate independent loading characteristic for the material

with a classical creep model as discussed in Section 111.3.

Repeated loading characteristics may be modelled simplywith moderate accuracy by means of a linear transformation

of the initial loading characteristic. This transform is a

function of residual strain and maximum strain as discussed

in Section III.4.

Material unloading characteristics, or hysteresis, maybe modelled by means of a generalized representation which

is a function of a normalized strain parameter. The

magnitude of the loads provided by this general rule is a

function of both maximum strain and strain rate as discussed

in Section 111.5.

The capability exists to generate additional similar

subroutine models for other parachute materials in short

times (one week of data processing) and from limited data

bases (digitized load and strain histories from ten drop

weight tests).

62

SECTION VII

RECOMMENDATIONS

The subroutine models developed should be used in avariety of parachute applications involving forced vibration

in an attempt to validate them for forced vibration problems

in general. The areas of stress, opening dynamics, and

stability analysis all promise such potential applications.

The subroutine models developed should be used to roughlymodel other similar materials. This could be done when

maximum accuracy is not required simply by scaling minimum

breaking strengths and strains. Experience in this area may

show that all materials covered by one Military Specification

can be represented by a single subroutine model which has

been normalized for minimum breaking strength and strain. For

example, one model might suffice to describe all the core-

sleeve nylon cords defined by MIL-C-5040E because of their

strong similarity in geometry of construction.

Since the mechanical properties of nylon materials canvary significantly from one lot to the next, specific sub-

routine models should be developed for particular applica-

tions. The time and data required to generate models are

sufficiently small to allow this approach. As an example,

during the development of a new spacecraft parachute recovery

system, a small number of samples could be taken from the

same material lots used to fabricate the parachute systems.

Subroutine models could be developed quickly from tests of

the material samples. This would allow accurate simulation

of system dynamics prior to full-scale development.

Consideration should be given to the generation oflibraries of subroutine models for many different parachute

components and materials. The benefits would be consider-

able for the general purposes of parachute recovery system

design and analysis.

63

Consideration should be given to development of sub-

routine models from free vibration load-time data alone.

Corresponding strain-time data could be generated by inte-

gration of the load-time data. This method would simplify

the design of the drop-weight test apparatus to be used and

reduce data acquisition requirements to the minimum.

Improvements to the math modelling approach outlined

in this report should include the following.

1. A refined creep model developed along the same lines

but from a larger data base to include the tertiary stage of

creep and more load levels. This would serve primarily to

improve low strain rate correlation.

2. The development and inclusion of material failure

criteria in the subroutine models. This may evolve directly

from development of an improved creep model.

3. The inclusion of temperature effects since these can

become even more significant than strain rate effects according

to Reference 20.

4. The development and inclusion of a relaxation model

following the form of the creep model already developed. This

would provide more realistic prediction of instantaneous

plastic strain than the simplistic method described in

Section III.4.

(20) Swallow, J.E., and Webb, Mrs. M.W., "Single and RepeatedSnatch Loading of Textile Yarns, and the Influence ofTemperature on the Dynamic Mechanical Properties", Journalof Applied Polymer Science, Vol. 8, pp. 257-282, 1964.

64

L

APPENDIX A

MODEL/DATA CORRELATION

65

APPENDIX A INDEX

TEST PAGE

iMi 68

2-2 70

3-3 72

4-1 74

5-3 76

6-1 78

7-2 80

8-2 82

9-2 84

10-3 86

11-1 88

2-C 90

3-C 92

iwi 94

2W1 96

3Wl 98

1W~4 100

1W5 102

6W3 104

3W7 106

8W2 108

9W2 110

16W 112

30W 114

1F 3 116

2F3 118

3F2 120

3F4 122

5F2 124

6F2 126

3F7 128

8F1 130

66

TEST PAGE

9F 3 132

3F1 134

3 OF 136

67

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CD210cr I I (

F-' L(2 m(0 a- CD C:) FLU CD CD 0) CE CF- Of~ LU z C

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APPENDIX B

SUBROUTINE LISTINGS

138

SUBROUTINE MODEL FOR

NYLON CORD, MIL-C-5040E'

TYPE II

139

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SUBROUTINiE MODEL FOR NYLON

FABRIC WARP, MIL-C-7020F

TYPE I

144

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REFERENCES

1. Priesser, J.S. and Green, G.C., "Effect of SuspensionLine Elasticity on Parachute Loads," Journal of'Space-craft and Rockets, Vol. 7, No. 10, Oct. 1970, pp., 1278.t1280.

2. Poole, L.R., "Effect of Suspension-Line Viscous Dampingon Parachute Opening Load Amplification,"' Journal ofSpacecraft and Rockets, Vol. 10, No. 1, Jan. 1973,pp. 92-93.

3. Mullins, W.M., et al., Investigation of PredictionMethods for the Loads and Stresses of Apolloffiyp SHace-craft Parachutes. Volume 2: S'tresses, NABA-CR-1342I1970.

4. Houmard, J.E. Stress Analysis of the Viking Parachute,AIMA Paper 73-444, 1973.

5. Reynolds, D.T., and Mullins, W.M., An Internal LoadsAnalysis for Ribbon Parachutes, NV75-12, NortropCorp., Ventura Division, 1975.

6. McVey, D.F., and Wolf, D.F., "Analysis of Deployment andInflation of Large Ribbon Parachutes," Journal of Air-'craft, Vol. 11, No. 2, Feb. 1974, pp. .96-103.

7. Ibrahim, S.K., and Engdahl, R.A., Parachute Dynamics andStability Analysis, NASA-CR-120326, Feb 1974.

8. Sundberg, W.D., Finite-Element Modelling of ParachuteDeployment and InElationH, AIMA Paper 15-16~3U, 1975.

9. Talay, T.A., Parachute-Deployment-Parameter Identifica-tion Based on an Analytical S-ation of Viking BLDTAV-4, NASA-TN-D1678, Aug. 1974.

10. Bobbitt, P.J., "Recent Advances and Remaining Voids inParachute Technology," AIMA Aerodynamic DecelerationSystems Tech Committee Position Paper, Astronautics andAeronautics, Oct. 1975, pp. 56-63.

11. McCarty, R.E., A Computer Subroutine for the Load-Elongation of Parachute Suspension Lines, XAM Paper75-136Z, 1975.

12. Keck, E.L., A Computer Simulation of Parachute OpeningDynamics, AIAA Paper 75-1379, 1973.

13. DeBoor, C., and Rice, J.R., Cubic Spline Approximation II-Variable Knots, Computer Science Department TRZZ1,Purdue University, April 1968.

161

14. Crandall, S,H., and Dahl, N.C,, An Introduction to theMechanic; of Solids, McGraw-Hill, 1959, pp. 222-223

15. Bruhn, E.F., Analysis and Design of Flight VehicleStructures, Tri-State Offset, 1965, pp. B1.12-13.

16. Polakowski, N.H.,and Ripling, E.J., Strength and Struc-ture of Engineering Materials, Prentice-Hall, 1966,p. 429.

17. Groom,J.J., Investigation of a Simple Dynamic Systemwith a Woven-Nyion ape Member Displaying NonlinearRamplng, Thesis for Master of Science, Ohio StateUniversity, 1974, pp. 51-54.

18. 777 Interactive Graphics System, Version 2.1, Referencea nual, Control Data Corporation publication number1732100, Revision B, 30 October 1975.

19. FORTRAN Extended, Version 4, Reference Manual, ControlData Corporation publication number 60305600, RevisionJ, 5 March 1976.

20. Swallow, J.E.,and Webb, Mrs. M.W., "Single and RepeatedSnatch Loading of Textile Yarns, and the Influence ofTemperature on the Dynamic Mechnaical Properties,"Journal of Applied Polymer Science, Vol.8, pp. 257-2821964.

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