TAM 224/CEE 210 6–1

6. Compression and Hardness Tests6.1. Objective Instrumented compression tests are performed on the same materials that were previously tested in tension. Indentation hardness tests are also conducted on these materials, using two different standard methods.

The objective is to learn not only what relations exist between the important tensile, compressive, and hardness properties for a given material, but also what the relative magnitudes of these properties are for different materials.

6.2. Apparatus

Compression Instrumented compression tests will be performed on cylindrical specimens (Fig. 1) using the Instron testing machines employed previously for the tensile

tests. Transparent shields that surround the specimen are provided for operator safety. A one-inch (25.4 mm) gage length extensometer is used to measure specimen contraction to a maximum strain of about –15%.

Hardness Industry-standard Brinell and Rockwell hardness testing machines are used to determine hardness.

A Brinell hardness test (Fig. 2) requires measuring the diameter of an indentation made by a 10-mm-dia. hardened steel ball. A standard load of 3000 kgf is

used for testing hard materials. The load may be reduced to 1500 kgf or 500 kgf for softer materials.

A Rockwell machine displays a number that is related to the depth of penetration of an indenter caused by a known load. For the Rockwell-B hardness test, for example, the indenter is a 1/16-in.-dia. hardened steel ball and the major load is 100 kgf.

The use of a Vickers microhardness tester may also be demonstrated. In this method, a very small load is applied by means of a pyramidal indenter, and the dimensions of the indentation are then measured using a microscope that is an integral part of the hardness tester.

L

d

Fig. 1. Nomenclature for compression specimens.

Fig. 2. Brinell hardness test.

6–2 Behavior of Engineering Materials TAM 224/CEE 210

6.3. Materials Materials to be tested include construction grades of steel and aluminum, as well as cast iron and PMMA. The specimens are solid cylinders, as shown in Fig. 1. Nominal dimensions of the specimens are given in the accompanying table:

6.4. Experimental Procedure Students may be divided into two or more groups so that compression and hardness testing can be done simultaneously.

Compression 1. Measure the diameter d of each specimen, taking

the average of three measurements, and begin filling out Table 1.

2. Set up the testing machine and extensometer following the general instructions given in Lab 6—The Tension Test.

3. Make sure an appropriate safety shield is in place around the specimen to protect personnel in the testing area.

4. Load the specimen until it undergoes noticeable plastic deformation or plastic buckling, or has failed, or until the capacity of the machine has been reached.

5. Observe and document any changes in the shape and appearance of each specimen as it is being deformed, as well as at fracture (if any).

Hardness 6. Perform Brinell hardness tests on the aluminum

specimens (and any other materials for which specimens are available). Begin filling out Table 2. For testing procedures, see the handout “Brinell Hardness Testing Machine Wilson Model J” available in the laboratory.

7. Perform Rockwell hardness tests on all the metal specimens. For testing procedures, see the handout “Rockwell Testing on the Wilson Model 523” available in the laboratory.

8. Observe the testing procedure for a Vickers hardness tester on one or more of the specimens provided. For testing procedures, see the handout “Leitz Mini-load (Vickers) Hardness Testing Machine” available in the laboratory.

6.5. Analysis of Results 1. Construct an engineering stress–strain curve for

each of the materials tested. Remember to label the axes as negative.

2. From the stress–strain curve of each material, compute: (a) the modulus of elasticity E, (b) the yield strength σ y , and (c) the ultimate strength σ u in compression. Begin filling out Table 3.

3. Construct a true stress–strain diagram for steel on the same graph for the engineering stress–strain curve.

4. Complete Table 3. Transfer data also to the appro-priate table of the Bending and Torsion Tests lab (Experiment 7 in this lab manual) for future reference.

5. Convert measured Rockwell hardness numbers to Brinell hardness numbers, using the conversion chart on the next page, and compare with measured Brinell harness numbers for the two materials tested by both hardness methods.

6. Using the data in Table 3, construct a plot of yield strength σ y as a function of Brinell hardness HB. Plot the yield data from both the tensile and compressive tests.

6.6. Points for Discussion Note.—Your lab instructor will indicate which of the

following questions are to be addressed in your report.

1. Compare the compressive behaviors (geometry of deformation, stress–strain curves, fracture modes) of the materials tested.

2. Compare the strength quantities and Young’s moduli for the various materials tested in compression.

3. Compare the ability of all the materials tested to undergo compressive nonrecoverable (plastic) deformation. Compare the final deformed shapes of the tensile and compressive tests. Are there any general trends?

Material d (mm) L (mm)

Steel 12.7 38.1

Aluminum 12.7 38.1

Cast iron 12.7 38.1

PMMA 19.1 63.5

TAM 224/CEE 210 Compression and Hardness Tests 6–3

4. Compare the compressive behavior of each material with its tensile behavior.

a. Do the stress–strain curves differ from the tension test ones?

b. Are the values of Young‘s modulus measured from tension and compression tests close to each other?

c. Are the values of yield strength and ultimate strength measured from tension and compres-sion tests close to each other? Is the ultimate strength in compression a well-defined parameter?

5. Compare the shape of stress–strain curves of PMMA in tension and compression. Does PMMA display a major difference in behavior between tension and compression? Discuss the ability of PMMA to undergo nonrecoverable deformation in each test.

6. Compare the true and engineering stress–strain curves for the steel. Is the absolute value of the true stress larger or smaller than that of the engineering stress? Why?

7. Can Rockwell and Brinell tests be used on PMMA? Why?

8. If a material such as a ceramic displays minimal inelastic (plastic) deformation in compression, would you expect the hardness measurement techniques used in this lab to be useful?

9. Determine if there is a correlation between yield strength and hardness of the materials tested. What would be the practical importance of such a correlation?

10. Determine if there is a correlation between ultimate tensile strength and hardness of the materials tested. What would be the practical importance of such a correlation?

11. Given that the Rockwell-B hardness number of a material is determined by the relation

HRB = −130 500δ ,

where δ is the depth of penetration (in mm) of the spherical indenter into the material, determine the depth of penetration for a structural steel having a hardness of, say, 90 HRB. What is the largest Rockwell-B number possible? In principle, can the Rockwell-B number be negative? Comment on all answers.

12. Given that the Brinell hardness number of a material is determined by the relation

Hardness Hardness HRC HB HRB HB

68 98 228 67 97 222 66 96 216 65 (739) 95 210 64 (722) 94 205 63 (705) 93 200 62 (688) 92 195 61 (670) 91 190 60 (654) 90 185 59 (634) 89 180 58 615 88 176 57 595 87 172 56 577 86 169 55 560 85 165 54 543 84 162 53 525 83 159 52 512 82 156 51 496 81 153 50 481 80 150 49 469 79 147 48 455 78 144 47 443 77 141 46 432 76 139 45 421 75 137 44 409 74 135 43 400 73 132 42 390 72 130 41 381 71 127 40 371 70 125 39 362 69 123 38 353 68 121 37 344 67 119 36 336 66 117 35 327 65 116 34 319 64 114 33 311 63 112 32 301 62 110 31 294 61 108 30 286 60 107 29 279 59 106 28 271 58 104 27 264 57 103 26 258 56 101 25 253 55 100 24 247 23 243 22 237 21 231

6–4 Behavior of Engineering Materials TAM 224/CEE 210

2 2

2HB P

D D D dπ=

− −

,

where P is the applied load (in kgf), D is the ball diameter (in mm) and d is the measured indenta-tion diameter (in mm), show that for small d , the formula reduces to

HB =42Pdπ

,

i.e. the Brinell hardness number is equal to the load divided by the projected area of contact, independent of the ball diameter D. On the other hand, what happens to the Brinell hardness number when the indenter simply punches through the material (i.e. d D→ )? Include illustrations with your discussion.

13. Given that the Vickers hardness number of a material is determined by the relation

HV =172

12

. Pd

,

where P is the applied load (in kgf) and d1 is the diagonal of the square pyramidal indentation (in mm), comment on the factor 1.72 appearing in the formula. What would the numerical value of this factor be if the projected area of contact were used in the calculation? (The formula that is used is actually based on the contact surface area formed by the pyramidal indenter, not the projected area of the indentation.)

14. Given that the Vickers hardness number of a material is determined by the relation

HV =172

12

. Pd

,

where P is the applied load (in kgf) and d1 is the diagonal of the square pyramidal indentation (in mm), calculate what the value of d1 must have been if a Vickers number of 400 was determined for a medium-strength steel with an indenter mass of 500 g (i.e. P = 0.5 kgf). (See Fig. 4, which illustrates the indent as it appears under the microscope.) How does the size of this indent compare with that of Brinell indentations in this laboratory?

15. Compare the relative merits and drawbacks of compression testing and hardness testing, by constructing a table like the following:

Under “nature” mention whether the method is destructive or nondestructive; under “ease of use” mention whether the method is quick and easy or involved and time-consuming; under “informa-tion provided” mention whether the method pro-vides detailed, abundant information or limited information useful only for comparison. Com-ment briefly on all entries you place in the table.

16. Are the Rockwell-B and Brinell hardness values you obtained for various materials consistent with each other? Use the hardness conversion chart to make direct comparisons, or refer to similar charts in other sources (for example, Fig. 6.13 of Callister 1985, or Fig. 2.22 of Flinn and Trojan 1990, or Fig. 5.1.22 of Marks' Handbook 1987.)

17. In their textbook, Ashby and Jones (1980) use the slipline theory of classical plasticity to derive an approximate formula for the hardness number of a material, based the material’s yield strength. Considering a hardness test of the Brinell or Vickers type, they calculate that the average pressure p under the indenter should be approximately

p y≅ 3σ ,

0

25

50

75

100

0 5 10 15

x

Indent

Fine scale Coarse scale

Microscopeview

d1

Fig. 4. Vickers microhardness indentation.

Method

Nature

Ease of use

Information provided

Compres-sion tests

Hardness tests

TAM 224/CEE 210 Compression and Hardness Tests 6–5

where σ y is the uniaxial yield strength of the material. Does it seem reasonable that a relation should exist between hardness (as measured by p ) and the yield strength of the material? If there is a relation like this, why is it not simply p y= σ ? Do your experimental results bear out Ashby and Jones’s prediction?

18. Explain how and why the gravitational constant g appears in the calculation of the pressure p exerted by the indenter on the material in the Brinell (and the Vickers) hardness tests, when this pressure is to be expressed in SI units (Table 2). Be careful to describe the manner in which the load is actually applied.

19. Explain why the Brinell hardness-testing method is commonly preferred in foundries that produce castings, whereas the Rockwell hardness-testing method is commonly preferred in heat-treating laboratories.

6.7. References Ashby, M. F., and D. R. H. Jones. 1980. Engineering

Materials—An Introduction to Their Properties and Applications. Oxford: Pergamon, 81, 105-106.

Avallone, E. A., and T. Baumeister III, eds. 1987. Marks’ Standard Handbook for Mechanical Engineers, 9th ed. New York: McGraw-Hill, Section 5.1.

Callister Jr., W. D. 2000. Materials Science and Engineer-ing—An Introduction, 5th ed. New York: Wiley, Sections 6.1–6.12.

Flinn, R. A., and P. K. Trojan. 1990. Engineering Materials and Their Applications. Boston: Houghton Mifflin, 113-116

Printed 7/9/03

6–6 Behavior of Engineering Materials TAM 224/CEE 210

Table 1—Compression and hardness data Measurement or property Material

Quantity Symbol Units ____ Steel PMMA _____ Al Cast iron

Initial data

Diameter d0 mm

Cross-sectional area A0 mm2

Gage length l0 mm

Strength data

Approximate yield load* Py kN

Approximate max. load* Pmax kN

Reason for stopping test

—

—

Detail of fracture surface or final shape

(sketch)

—

—

Hardness—Rockwell B (1/16” ball, 100 kgf)

Observed hard- 1st HRB —

ness readings 2nd HRB —

(uncorrected for 3rd HRB —

curvature) Avg HRB —

Correction for curvature* HRB —

Rockwell hardness HRB —

Brinell hardness (converted) HB kgf/

mm2

*For the Rockwell B scale, if the specimen diameter is 0.5 in. (13 mm), the correction (which is to be added to the observed Rockwell B reading) is given by the linear relationship (adapted from Wilson conversion chart):

Correction HRBuncorrected= − ×6 5 0 05. . .

For example, if the observed Rockwell B hardness reading is 80 HRB on the cylindrical surface of a 0.5-in.-dia. specimen, the curvature correction is equal to +2.5 HRB, and thus the corrected Rockwell B number is 82.5 HRB. The value of the curvature correction is rounded to the nearest multiple of 0.5.

TAM 224/CE 210 Compression and Hardness Tests 6–7

Table 2a—Hardness data (individual student)

Measurement or property Material

Quantity Symbol Units ____ Steel _____ Al

Hardness—Brinell (ball diameter D = 10 mm; indenter load = 3000 kg)

Diameter of indent d mm

Brinell hardness number HB kgf/ mm2

Hardness—Rockwell B and C

Rockwell B hardness number HRB —

Rockwell C hardness number HRC —

Table 2b—Comparative hardness data (lab section average)

Measurement or property Material

Quantity Symbol Units ____ Steel _____ Al

Hardness—Brinell (ball diameter D = 10 mm; indenter load = 3000 kg)

Brinell hardness number HB kgf/ mm2

Hardness—Rockwell B and C

Rockwell B hardness number HRB —

Rockwell C hardness number HRC —

Brinell hardness (converted from Rockwell B or C hardness)

Converted Brinell hardness number HB kgf/

mm2

6–8 Behavior of Engineering Materials TAM 224/CEE 210

Table 3—Summary of results

Mechanical property Material

Quantity Symbol Units ____ Steel PMMA _____ Al Cast iron

Tensile properties (from Tensile Test Lab)

Young’s modulus E GPa

Yield strength σ y MPa

Ultimate strength σ u MPa

Percent elongation %EL —

Shape changes during deformation

— —

Nature of fracture surface

— —

Compression properties

Young’s modulus E GPa

Yield strength σ y MPa

Ultimate strength σ u MPa

Shape changes during deformation

— —

Nature of fracture surface

— —

Hardness

Rockwell (corrected for curvature) HRB —

Brinell (converted) HB kgf/ mm2

Brinell—SI force units* p g= ⋅HB MPa

Slipline theory p y≅ 3σ MPa

Test date(s): Student’s name(s):

*Use g = 9.81 m/s2.

Printed 7/9/03