ANALYSIS OF STRESS DISTRIBUTION ON … · profiles later and again subjected to various loading conditions and ... the variation of failure ... resultant residual force prevailing

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International Journal of Mechanical Engineering and Technology (IJMET) Volume 8, Issue 7, July 2017, pp. 897–908, Article ID: IJMET_08_07_098

Available online at http://www.iaeme.com/IJMET/issues.asp?JType=IJMET&VType=8&IType=7

ISSN Print: 0976-6340 and ISSN Online: 0976-6359

© IAEME Publication Scopus Indexed

ANALYSIS OF STRESS DISTRIBUTION ON

DIFFERENT SECTIONS UNDER DIFFERENT

LOADING AND MACHINING CONDITIONS

K L N Sandeepa Sarma, B. Venkateshwarlu, Jacob Thottathil Varghese

School of Mechanical Engineering,

Vellore Institute of Technology, Vellore, India

ABSTRACT

The magnitude of stress is directly proportional to strain up to yield point

particularly in thick walled components. The distortion of components is strongly

related to the residual stresses induced by manufacturing processes like forming and

machining. While removing material during machining, new stress state of equilibrium

is established in the component. The product quality and efficiency during

manufacturing can be increased by thorough understanding of stress distribution under

different loading and machining conditions. In this work, welded T, I, and L profile

sections made of pure aluminium used as test specimens. Grooves were machined to the

profiles later and again subjected to various loading conditions and results were

obtained. Different loads of 30, 35, and 40 kN were applied on purely welded

components and machined and welded components. The corresponding pressure

distribution results were compared. It was observed that effect of machining is different

for different sections. Purely welded T and I sections are weaker compared to their

machined and welded counterparts whereas purely welded L-sections are stronger

compared to their machined and welded counterparts.

Key words: Distortion, Finite element method (FEM), Machining, Residual stresses.

Cite this Article: K L N Sandeepa Sarma, B. Venkateshwarlu and Jacob Thottathil

Varghese, Analysis of Stress Distribution on Different Sections Under Different

Loading and Machining Conditions, International Journal of Mechanical Engineering

and Technology, 8(7), 2017, pp. 897–908, 8(7),

http://www.iaeme.com/IJMET/issues.asp?JType=IJMET&VType=8&IType=7

1. INTRODUCTION

I, L, and T sections are frequently used in various structural units such as bridges, railway

tracks, etc., and also to support various complex geometric structures. This implies that these

sections are subjected to very high pressures and moments. The distortion of components is

strongly related to residual stress state induced by manufacturing process like forming and

machining. It is clear that there is a significant influence of mechanical operations done a

component on the residual stress distribution which acts as a carrier of distortion potential [1].

K L N Sandeepa Sarma, B. Venkateshwarlu and Jacob Thottathil Varghese


It is concluded in one of the previous works that heterogeneous residual stresses increase

amount of distortion [2]. The correlation exists between residual stresses and amount of

distortion in an increasing fashion as observed for a grinding process [3]. While removing

material during machining, new stress equilibrium is established for the component [4]. The

stress is directly proportional to the strain up to yield point. Beyond yield point, particularly in

thick walled cylinders, there exists a phase in which material is partially elastic and partially

plastic. Perfect plasticity is a property of materials to undergo an irreversible plastic

deformation without any increase in stresses when loads are applied. Plastic materials with

hardening necessitate increasingly higher stresses to result in further plastic deformation. The

two phases will meet at a junction point and state exists till whole material becomes plastic with

an increase in pressure. This intermediate phase is called an elastic-plastic phase. In cylindrical

components subjected to high internal pressures, the plastic state is represented by power law

which is expressed as � = �� ∈n, where �� is strain hardening modulus, n is index (from 0 to

1). According to Brinksmeier et al. 2009 [5], the distortion potential is related to residual

stresses induced in the components during manufacturing process.

2. EXPERIMENTAL PROCEDURE

The work pieces have been designed, welded and machined using CATIA V5R17 software. Six

work pieces are used in this work and named as 1.Welded L-section, 2. Machined and welded

L-section, 3.Welded T-section and 4.Machined and welded T-section 5. Welded I-section 6.

Machined and welded I-section (see Figures 1- 6).

Figure 1 Geometry of purely welded L-section

Figure 2 Geometry of machined and welded L-section

Figure 3 Geometry of purely welded T-section

Figure 4 Geometry of machined and welded T-section

Analysis of Stress Distribution on Different Sections Under Different Loading and Machining

Conditions


Figure 5 Geometry of machined and welded I-section

Figure 6 Geometry of purely welded I- section

The specimens are manufactured from aluminium blocks of 120 x 60 x 20 mm size. For

purely welded components, the blocks are maintained in their respective planes and welded

correspondingly. For machined and welded components, a groove of 20 X 60 x 10 mm size is

made at centre of the base block using lathe machine and then the other block is fitted into the

groove and welded. Each work piece is subjected to a load of 30, 35, and 40 kN and the

corresponding pressure induced on work piece surface is computed using the simple relation

P=F/A, where F= Force applied on work piece surface (kN), A= Surface area of the work piece

subjected to loading (mm2). Profiles are meshed and finite element method (FEM) techniques

are applied. The reports are generated using above mentioned software. Results obtained for

purely welded and machined and welded components are compared and analyzed.

3. MODELLING WITH CATIA

For the work piece, the material behaviour of tempered aluminium is modelled using

viscoelastic-plastic behaviour. Yield stress is calculated using below mentioned analytical

function [6]

(1)

The yield stress depends on the equivalent plastic strain Ɛpl and also the temperature for

including thermal softening effects. A, B, m and n are material parameters. The non-

dimensional temperature Ɵ is calculated with the current temperature. The strain rate

dependence is expressed by the middle term, where C is the dimensionless strain-rate hardening

coefficient and Ɛ0 is the normalizing reference strain rate. The material parameters used in this

work for modelling are shown in below Table 1 [7-9]. For designing and machining, CATIA

V5R17 software is used. Using this software various machining operations such as milling,

welding, all lathe operations, etc., can be done with high degree of accuracy. Specimens are

clamped rigidly and the load is applied on appropriate surfaces. After meshing is done, stress

and strain distributions are evaluated and the corresponding plots are generated.



Table 1 Material parameters used for modelling

A [MPa] 546 Tm [K] 922

B [MPa] 678 Ttr [K] 293

C 0.024 Ρ [g/cm3] 2.7

M 1,56 cv [J/kg-K] 896

n 0.71 G [GPa] 26.5

Ɛ0[1/s] 1 E [GPa] 79.4

In this work, finite element method and von misses criterion is applied to the work pieces.

The main criterion chosen for failure is maximum strain energy criterion or von misses failure

criteria, which says that the material will fail when the equivalent stress exceeds the yield point

of the material. For an axis-symmetric problem, there are no shear stresses induced and hence

hoop, longitudinal and radial stresses are the principal stresses. The governing equation

considered for failure for this situation is:

(2)

Where, σƟ is hoop stress, σr is radial stress, σz is stress along z-axis and σy is normal stress

[6]. Here, left hand side of the governing equation represents von Mises stress. The work piece

models used for analysis are shown below in Figure 7.

Figure 7 CATIA workpiece models of L-section

4. ANALYSIS RESULTS

Loading condition at 30 kN: The corresponding maximum pressure applied on surface is

4166666.6667 N/m2 (see Figures 8-13)

Figure 8 Purely welded L-section.


Conditions


Figure 9 Machined and welded L-section.

Figure 10 Purely welded T-section

Figure 11 Machined and welded T-section.

Figure 12 Purely welded I-section



Figure 13 Machined and welded I-section

4.2. Loading condition at 35 kN: The corresponding maximum pressure applied on surface is

4861111.1111 N/m2 (see Figures 14-19)

Figure 14 Purely welded L-section

Figure 15 Machined and welded L-section

Figure 16 Purely welded T-section


Conditions


Figure 17 Machined and welded T-section


Figure 19 Machined and welded I-section.

4.3. Loading condition at 40 kN: The corresponding maximum pressure applied on surface is

5555555.556 N/m2 (see Figures 20-25).

Figure 20 Purely welded L-section.



Figure 21 Machined and welded L-section

Figure 22 Purely welded T-section.

Figure 23 Machined and welded T-section.



Conditions


Figure 25 Machined and welded I-section.

5. RESULTS AND DISCUSSION

The figures 8-25 show the analysis results obtained for L, T and I sections subjected to various

loading conditions before and after suitable machining. The figures show mesh plots with

different colours where red colour indicates maximum stress level (i.e. failure stress), blue

colour indicates minimum stress and green colour indicates permissible stress levels.

Figure 26 Load Vs Failure stress for L-section

L- section: The above graph (see Figure 26) indicates the variation of failure stress level for L-

section. Series 1 is for purely welded L section and series 2 is for machined and welded L

section. From the above figure, it can be seen clearly that purely welded L-section can bear

more stress before its failure compared to the corresponding welded and machined section. This

may be attributed to weakening of machined section because of residual stresses induced during

machining. In case of L section, it can also be seen that the complete stress is borne by the

machined part and fails easily.

Table 2 Magnitude of residual forces for L-section

Force (kN) For purely welded section For welded and machined

section

30 1.809*10^-4 4.896*10^-4

35 2.004*10^-4 8.232*10^-4

40 2.836*10^-4 9.427*10^-4



The table 2 shows the magnitude of the resultant residual force prevailing at each loading

condition for purely welded and welded and machined L-section. The magnitude of resultant

force (RF) is computed using the following relation,

RF = (Fx2+Fy

2+Fz2)0.5 (3)

Where, FX, FY and Fz are the magnitude of residual forces along X, Y, and Z directions

respectively and RF is the resultant residual force.

Figure 27 Load Vs Failure stress for T-section

T-section: The above graph (see Figure 27) indicates the variation of failure stress level for T-

section. Series 1 is for purely welded T section and series 2 is for machined and welded T

section. From the above figure, it can be seen that machined and welded T-section can bear

more stress before its failure as compared to the corresponding purely welded section. Here, T

section groove is in symmetric position which adds additional support and gives more strength

to the section. Table 3 shows the magnitude of the residual force prevailing at each loading

condition for purely welded and welded and machined T-section.

Table 3 Magnitude of residual forces for T-section

Force (kN) For purely welded section For welded and machined

section

30 1.139*10^-5 4.028*10^-5

35 2.5*10^-4 16.99*10^-4

40 0.09*10^-4 1.713*10^-4

The variation of failure stress level for I-section is shown in figure 28. Series 1 is for purely

welded I section and series 2 is for machined and welded I section. It can be seen that the

machined and welded I-section can bear more stress compared to the purely welded I-section.

The table 4 shows the magnitude of the residual force prevailing at each loading condition.


Conditions


Figure 28 Load Vs Failure stress for I-section

Table 4 Magnitude of residual forces for I-section

6. CONCLUSIONS

This paper presents the details of stress distribution at different magnitudes of load in purely

welded and welded and machined L, T and I sections. The following conclusions can be drawn

from this work:

• The machined components will be subjected to residual stresses due to machining operations.

It can be concluded that for a given loading conditions, the machined and welded components

can bear more residual forces compared to the purely welded components (From Table 2 and

Table 3). This is due to reduction of material in the area of machining and prevailing residual

stresses (i.e., machined (grooved) component has high residual stress).

• It can be seen that machined and welded L-components fail faster than the purely welded L-

components and purely welded T-components fail faster than the machined and welded T-

components. It can also be seen that purely welded I-section fail faster as compared to the

machined and welded I-sections.

• From the obtained results it can be observed that the effect of machining (here grooving) varies

for a different sections. In this case, T-section has got an increment in strength due to machining

while there was a decrement in strength for the L-section.

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Force(kN) Purely welded Machined and welded

30 2.139*10^-5 5.028*10^-5

35 3.5*10^-4 17.99*10^-4

40 1.09*10^-4 2.713*10^-4



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ANALYSIS OF STRESS DISTRIBUTION ON … · profiles later and again subjected to various loading conditions and ... the variation of failure ... resultant residual force prevailing