ASM Metals HandBook Vol. 8 - Mechanical Testing and Evaluation

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Fig. 19 Circumferentially notched torsion specimen for mode III fatigue crack propagation. Dimensions

are in mm. r

, outer radius; r

, radius of notch. Source: Ref 17

Tubular Specimen Containing a Slit. This type of specimen is used to investigate the fatigue crack growth

behavior and approximately two-dimensional, mixed-mode stress condition under torsion coupled with tension-

compression. A typical initial notch (Fig. 20) is usually introduced. The width of slit must be very small,

because the initial geometry of the slit strongly influences the initial direction of crack growth.

Fig. 20 Tubular specimen containing a slit for combined torsion and tension-compression fatigue test.

Dimensions are in mm. Source: Ref 18

Solid Cylindrical Specimen Containing a Small Hole or Initial Crack. The effects of artificial small defects on

torsional fatigue strength can be studied by introducing an artificial small hole (Ref 4). Figure 21 shows the

shape and dimension of a drilled hole.

Fig. 21 Shape and dimension of a small hole introduced on the surface of torsional fatigue test specimen.

(Geometry of specimen is shown in Fig. 4.) d, diameter. Source: Ref 4

If a fatigue crack is introduced by a preliminary tension-compression fatigue test, crack growth behavior and

threshold condition under mixed-mode loading can be studied. Initial small semielliptical cracks ranging from

200 to 1000 μm in length are introduced by preliminary tension-compression fatigue using a specimen

containing holes of 40 um diameter (Fig. 22). Crack growth behavior from the initial small crack, such as crack

branching (Ref 1) and kinking (Ref 19), can be investigate. The threshold condition of a small crack can be

studied based on the mixed-mode fracture mechanics analysis of a semielliptical crack (Fig. 3).

Fig. 22 Initial small surface crack introduced by tension-compression fatigue test using the specimens

containing holes of 40 μm. (Geometry of specimen is shown in Fig. 7.) Source: Ref 1

References cited in this section

1. Y. Murakami and K. Takahashi, Torsional Fatigue of a Medium Carbon Steel Containing an Initial

Small Surface Crack Introduced by Tension-Compression Fatigue: Crack Branching, Non-Propagation

and Fatigue Limit, Fatigue Fract. Eng. Mater. Struct., Vol 21, 1998, p 1473–1484

4. M. Endo and Y. Murakami, Effects of an Artificial Small Defect on Torsional Fatigue Strength of

Steels, J. Eng. Mater. Technol. (Trans. ASME), Vol 109, 1987, p 124–129

6. S. Iida and A.S. Kobayashi, Crack-Propagation Rate in 7075-T6 Plates under Cyclic Tensile and

Transverse Shear Loadings, J. Bas. Eng. (Trans. ASME), Ser. D, Vol 91, 1969, p 764–769

7. K. Tanaka, Fatigue Crack Propagation from a Crack Inclined to the Cyclic Tensile Axis, Eng. Fract.

Mech., Vol 6, 1974, p 493–507

8. A. Otsuka, K. Mori, and T. Miyata, The Condition of Fatigue Crack Growth in Mixed-Mode Condition,

Eng. Fract. Mech., Vol 7, 1975, p 429–439

9. H. Kitagawa, R. Yuuki, and K. Tohgo, A Fracture Mechanics Approach to High-Cycle Fatigue Crack

Growth Under In-Plane Biaxial Loads, Fatigue Eng. Mater. Struct., Vol 2, 1979, p 195–206

10. H. Gao, M.W. Brown, and K.J. Miller, Mixed-Mode Fatigue Thresholds, Fatigue Eng. Mater. Struct.,

Vol 5, 1982, p 1–17

11. K. Tohgo, A. Otsuka, and M. Yoshida, Fatigue Behavior of a Surface Crack under Mixed Mode

Loading, Fatigue '90, Proc. of the 4th International Conf. on Fatigue and Fatigue Thresholds, Vol 1,

Materials and Component Engineering Publication, 1990, p 567–572

12. H.A. Richard and K. Benitz, A Loading Device for the Creation of Mixed Mode in Fracture Mechanics,

Int. J. Fract., Vol 22, 1983, p R55–R58

13. D.L. Jones and D.B. Chisholm, An Investigation of the Edge-Sliding Mode in Fracture Mechanics, Eng.

Fract. Mech., Vol 7, 1975, p 261–270

14. K. Komai and E. Usuki, Fractographic Study on Mode II and Mode III SCC Crack Growth in Al-Zn-Mg

Alloy, J. Soc. Mater. Sci., Jpn., Vol 33, 1984, p 921–926

15. Y. Murakami and S. Hamada, New Method for the Measurement of Mode II Fatigue Threshold Stress

Intensity Factor Range ΔK

IIth

, Fatigue Fract. Eng. Mater. Struct., Vol 20, 1997, p 863–870

16. Y. Murakami, C. Sakae, and S. Hamada, Mechanism of Rolling Contact Fatigue and Measurement of

ΔK

IIth

for Steels, Proc. of Engineering Against Fatigue, A.A. Balkema, Rotterdam, 1999

17. H. Nayeb-Hashemi, F.A. McClintock, and R.O. Ritchie, Effect of Friction and High Torque on Fatigue

Crack Propagation in Mode III, Metal. Trans. A, Vol 13A, 1982, p 2197–2204

18. A.T. Yokobori, Jr., T. Yokobori, K. Sato, and K. Syoji, Fatigue Crack Growth under Mixed Mode I and

II, Fatigue Fract. Eng. Mater. Struct., Vol 8, 1985, p 315–325

19. Y. Murakami and K. Takahashi, Crack Branching and Threshold Conditions of Small Cracks in Biaxial

Fatigue, Proc. of the 12th Biennial Conf. on Fracture, ECF 12, EMAS Publishing, Vol 1, 1998, p 67–72

Multiaxial Fatigue Testing

Yukitaka Murakami, Kyushu University, Japan

Summary

Since no standard testing method exists, it is important to choose a testing method suitable for a purpose of each

testing. Various testing methods available for biaxial and multiaxial fatigue testing are summarized as follows.

Biaxial fatigue testing machines, in which cyclic torsion is coupled with tension-compression loading, have

been widely used because these testing machines can be applied to study the following:

• Mode III crack growth behaviors under cyclic torsion by using circumferentially notched cylindrical

specimens

• Crack growth behaviors under approximately two-dimensional mode I and by using a tubular specimen

with a slit

• Effects of small fatigue crack or defect under biaxial loading if an initial small crack is introduced by

preliminary tension-compression fatigue testing

Triaxial Testing. In addition, biaxial fatigue testing (cyclic torsion with tension-compression) can be combined

with the application of internal or external pressure for tubular specimens or cylindrical specimens. The

influence of complex three-dimensional stress conditions can be investigated. However, these triaxial testing

machines are very complicated and expensive.

Notched Plate and Precracked Bending Specimens. Rectangular plate specimens with an inclined notch or a

crack and three-point or four-point bending specimens with a crack are used to investigate crack growth under

mixed mode I and II. It must be noted that the stress intensity factors cannot be kept constant during the test,

because crack growth mode shifts from mode II or III to mode I.

The cruciform specimen permits a wide variation of stress intensity factors, K

and K

. However, testing

machines for this type of specimen are complex, and preparation of specimens is not easy. High compressive

loads cannot be applied to the specimen because of the possibility of buckling.

Compact Specimen. The compact tension-shear (CTS) specimen is used to investigate the crack growth under

mixed mode I and II, including pure mode II, loadings. The compact shear (CS) specimen is also used to

investigate the crack growth under mode II and mode III. However, it is very difficult to achieve pure mode II

crack growth by these specimens because crack growth mode easily switches from mode II to mode I. Thus,

mode of loading is not necessarily the same as mode of crack growth.

Double Cantilever Specimen. Mode II crack growth plays an important role in crack growth under rolling

contact fatigue. The values of ΔK

IIth

for various steels can be measured using the specially designed double

cantilever specimen. A conventional closed-loop tension-compression fatigue testing machine can be used in

the system.

Multiaxial Fatigue Testing

Yukitaka Murakami, Kyushu University, Japan

References

1. Y. Murakami and K. Takahashi, Torsional Fatigue of a Medium Carbon Steel Containing an Initial

Small Surface Crack Introduced by Tension-Compression Fatigue: Crack Branching, Non-Propagation

and Fatigue Limit, Fatigue Fract. Eng. Mater. Struct., Vol 21, 1998, p 1473–1484

2. A. Ono, “Fatigue of Steel under Combined Bending and Torsion,” Mem. Coll. Eng., Kyushu Imp.

Univ., Vol 2, 1921, p 117–145

3. M.A. Fonte and M.M. Freitas, Semi-Elliptical Crack Growth Under Rotating or Reversed Bending

Combined with Steady Torsion, Fatigue Fract. Eng. Mater. Struct., Vol 20, 1997, p 895–906

4. M. Endo and Y. Murakami, Effects of an Artificial Small Defect on Torsional Fatigue Strength of

Steels, J. Eng. Mater. Technol. (Trans. ASME), Vol 109, 1987, p 124–129

5. M.W. Brown and K.J. Miller, Biaxial Cyclic Deformation Behavior of Steels, Fatigue Eng. Mater.

Struct., Vol 1, 1979, p 93–106

6. S. Iida and A.S. Kobayashi, Crack-Propagation Rate in 7075-T6 Plates under Cyclic Tensile and

Transverse Shear Loadings, J. Bas. Eng. (Trans. ASME), Ser. D, Vol 91, 1969, p 764–769

7. K. Tanaka, Fatigue Crack Propagation from a Crack Inclined to the Cyclic Tensile Axis, Eng. Fract.

Mech., Vol 6, 1974, p 493–507

8. A. Otsuka, K. Mori, and T. Miyata, The Condition of Fatigue Crack Growth in Mixed-Mode Condition,

Eng. Fract. Mech., Vol 7, 1975, p 429–439

9. H. Kitagawa, R. Yuuki, and K. Tohgo, A Fracture Mechanics Approach to High-Cycle Fatigue Crack

Growth Under In-Plane Biaxial Loads, Fatigue Eng. Mater. Struct., Vol 2, 1979, p 195–206

10. H. Gao, M.W. Brown, and K.J. Miller, Mixed-Mode Fatigue Thresholds, Fatigue Eng. Mater. Struct.,

Vol 5, 1982, p 1–17

11. K. Tohgo, A. Otsuka, and M. Yoshida, Fatigue Behavior of a Surface Crack under Mixed Mode

Loading, Fatigue '90, Proc. of the 4th International Conf. on Fatigue and Fatigue Thresholds, Vol 1,

Materials and Component Engineering Publication, 1990, p 567–572

12. H.A. Richard and K. Benitz, A Loading Device for the Creation of Mixed Mode in Fracture Mechanics,

Int. J. Fract., Vol 22, 1983, p R55–R58

13. D.L. Jones and D.B. Chisholm, An Investigation of the Edge-Sliding Mode in Fracture Mechanics, Eng.

Fract. Mech., Vol 7, 1975, p 261–270

14. K. Komai and E. Usuki, Fractographic Study on Mode II and Mode III SCC Crack Growth in Al-Zn-Mg

Alloy, J. Soc. Mater. Sci., Jpn., Vol 33, 1984, p 921–926

15. Y. Murakami and S. Hamada, New Method for the Measurement of Mode II Fatigue Threshold Stress

Intensity Factor Range ΔK

IIth

, Fatigue Fract. Eng. Mater. Struct., Vol 20, 1997, p 863–870

16. Y. Murakami, C. Sakae, and S. Hamada, Mechanism of Rolling Contact Fatigue and Measurement of

ΔK

IIth

for Steels, Proc. of Engineering Against Fatigue, A.A. Balkema, Rotterdam, 1999

17. H. Nayeb-Hashemi, F.A. McClintock, and R.O. Ritchie, Effect of Friction and High Torque on Fatigue

Crack Propagation in Mode III, Metal. Trans. A, Vol 13A, 1982, p 2197–2204

18. A.T. Yokobori, Jr., T. Yokobori, K. Sato, and K. Syoji, Fatigue Crack Growth under Mixed Mode I and

II, Fatigue Fract. Eng. Mater. Struct., Vol 8, 1985, p 315–325

19. Y. Murakami and K. Takahashi, Crack Branching and Threshold Conditions of Small Cracks in Biaxial

Fatigue, Proc. of the 12th Biennial Conf. on Fracture, ECF 12, EMAS Publishing, Vol 1, 1998, p 67–72

Introduction to Mechanical Testing of Components

Introduction

TESTING OF COMPONENTS requires an understanding of service conditions and mechanical testing and

design. While there are many types of components tests for a multitude of products, the articles in this Section

focus primarily on the basic principles for some common types of engineering components. These articles

provide an overview of the typical test methodology, developed by national organizations such as ASTM, as

well as industry-specific organizations, test apparatus, procedures, test sample preparation, data collection, and

interpretation. Using standard test methods provides for consistent test results.

The mechanical evaluation of components requires an engineer to use many sources of information. It also

requires an understanding of service conditions, design, and manufacturing variables. All these variables can

make it difficult to validate components. The following overviews briefly summarize some general factors in

the design and manufacture of components. Additional information is also provided in the article“Overview of

Mechanical Properties and Testing for Design” in this Volume. The remaining articles in this Section describe

tests for common types of fabricated components and the modeling of metal deformation.

Introduction to Mechanical Testing of Components

Overview of Component Testing

Brian Klotz, Component Test Resources, General Motors Corporation

Testing of components involves a series of processes to validate the product for usage. Computer systems are

playing a dominating role in the design of components and simulating how they react under different

environments. Design engineers use three-dimensional modeling software to design components. This software

allows the engineer to create a three-dimensional image of the component to scale. He or she can then

manipulate the image to identify design concerns, match to models of mating parts to check for interference,

and manufacture the component right from the model. This design model can also be used to generate a finite-

element analysis (FEA) model. The FEA model can show an engineer how the design reacts under various

loading conditions. If areas of the design are suspect, design changes can be made and reevaluated easily. While

FEA models provide an engineer the ability to improve component designs without making a physical part,

further test simulations to evaluate durability need to be developed to accurately predict the total capability of a

component. The use of physical tests is required to develop these simulations.

An understanding of the operating environment in which the component must function establishes the basis for

testing the component. The environment may include cyclic or static loading, vibration concerns, thermal

variations, or many others. Duplicating or simulating this environment becomes a challenge at a component

level. While elaborate test systems can be produced to incorporate multiple environments, in most instances the

basic component design functionality is all that need be evaluated. Developing tests to perform the evaluations

typically involves developing a set of fixtures to hold the component and impart the loading into the part on

some type of test stand. Design of fixtures is critical to the repeatability of the overall testing. The loading

characteristics the component experiences in its application must be understood in order for a test to be

developed.

Once the test environment is understood, fixtures developed, and the component design manufactured, a test

can be performed on the component. The testing is done either to correlate the output of the FEA model or

validate the component design and manufacturing. Testing done to compare the results from math-based FEA

models to real-life test results allows engineers the ability to further develop the capability of the models to

predict design concerns. This type of testing typically requires less samples and can provide long-term cost

benefits to an organization. This iterative process of design analysis and testing ultimately leads to product

designs that may require no component testing, only testing as part of an assembly to validate the system.

Testing done to validate the component design and manufacturing requires knowledge of the duty cycle in

which the component must operate. In order to develop component-level validation tests, test procedures and

methods must be correlated to this duty cycle, and the test stand must be able to duplicate these load inputs.

Validation tests require multiple samples to be subjected to duty-cycle loading. Results of these tests are then

evaluated using statistical methods in order to determine whether they meet the product design requirements.

This method of testing can be very costly if several redesigns must be done.

Introduction to Mechanical Testing of Components

Overview of Mechanical Properties for Component Design

Henry E. Fairman, MQS Inspection, Inc.

The ultimate result of performing mechanical tests is to provide information that may be used in the design and

manufacture of components. Design of components requires an understanding of the materials properties and

how they will be used by the component. The manufacturing process that is used to produce the part also must

be considered during the design process because manufacturing methods influence materials properties and the

selection of appropriate mechanical testing methods to ensure that the component will meet its required life

cycle.

This overview briefly reviews the relationship of mechanical properties in the process of mechanical design. As

previously noted, detailed materials properties and design methodologies are required for a wide variety of

applications that encompass factors such as:

• Load-bearing capability to meet the desired service condition

• Capability of the design to meet the required lifetime

• Effect of service (environmental) conditions on the design

• Performance requirements such as minimum weight, stiffness, and life-cycle cost

• Size and shape factors

A significant part of the design process is also the experience based on the performance of similar components.

The design process also uses predictive models, which may be a simple model or a more complex model

developed by the FEA method.

Introduction to Mechanical Testing of Components

General Mechanical Behavior

One key aspect of product and process design is a basic understanding of fundamental mechanical behavior,

which is described in the first two articles of this Volume (“Introduction to the Mechanical Behavior of Metals”

and “Introduction to the Mechanical Behavior of Nonmetallic Materials”). In general, fine-grained materials

have better mechanical and fatigue properties than coarse-grained materials. Components that have a mixture of

fine- and coarse-grained materials will generally have properties similar to those of the coarse-grained material.

Coarse-grained materials exhibit the lowest properties with the exception of creep and stress rupture, where

single-grained materials have exhibited superior properties at elevated temperature.

Nonuniform microstructures will affect the mechanical properties of the material or component. For example,

the center of 8 in. carbon or alloy bar produced by the strand casting process will exhibit different mechanical

properties than samples taken from the center, midradius, and outer diameter when tested in the longitudinal

direction. Samples taken from the transverse direction will also have different properties than the longitudinal

samples will have. Impact and fracture testing results are significantly impacted by the sample direction.

Mechanical working such as the rolling or drawing of materials can significantly improve the mechanical

properties of the materials, raising the yield and ultimate strengths along with reducing the ductility values. Age

hardening of metals generally raises the yield and ultimate strengths of materials. The fatigue properties are not

generally significantly improved by age hardening.

Heat treating processes that result in transformation hardening, such as occurs with carbon and alloy steels, will

raise the mechanical and fatigue properties of these alloys. It changes the creep properties by only a small

degree because the principal effect is in the initial stage of creep deformation.

Introduction to Mechanical Testing of Components

Properties and Design for Static Loads

Tension and compression testing are common test methods as described in detail in the articles “Uniaxial

Tension Testing” and “Uniaxial Compression Testing” in this Volume. Property data present in the literature

are normally based on specimens machined from raw materials and represent ideal data for the materials.

Typical stress-strain data for a variety of alloys are provided in Fig. 1. In the elastic region, stress and strain are

proportional by Hooke's law (σ = Eε). In the plastic region, work hardening is described by a power law:

σ = Ke

(Eq 1)

where K is the strength coefficient and n is the strain-hardening exponent. Typical stress-strain properties

values are shown in Tables 1 and 2 (Ref 1) for selected steels and aluminum alloys, respectively, for monotonic

loads. Tables 1 and 2 also list cyclic stress-strain properties, as described later. General properties related to

monotonic stress-strain behavior are described briefly here.

Table 1 Monotonic and cyclic stress-strain properties of selected steels

Elastic

modulus (E)

Yield

strength (S

)

Tensile

strength (S

)

Strength

coefficient (K)

True

fracture

stress (σ

)

Alloy Condition

(a)

GPa 10

ksi MPa ksi MPa ksi MPa ksi

Strain

hardening

exponent

(n)

Reduction

in area,

MPa ksi

True

fracture

strain

(ε

)

Monotonic properties

(b)

A136 As-received 207 30 321 46.5 556 80.6 993 144.0 0.21 67 990 143.6 1.06

A136 150 HB 207 30 317 46.0 565 81.9 … … 0.21 69 1000 145.0 1.19

SAE950X As-received, 137 HB 207 30 432 62.6 523 75.8 654 94.9 0.11 54 … … …

SAE950X As-received, 146 HB 207 30 391 56.7 510 74.0 800 116.0 0.15 74 978 141.8 1.34

SAE980X Prestrained, 225 HB 193 28 576 83.5 695 100.8 992 143.9 0.13 68 1219 176.8 1.15

1006 Hot rolled, 85 HB 207 30 248 36.0 318 46.1 414 60.0 0.14 73 … … …

1020 Annealed, 108 HB 186 27 254 36.8 392 56.9 399 57.9 0.07 64 661 95.9 1.02

1045 225 HB 200 29 516 74.8 751 108.9 1047 151.8 0.12 44 998 144.7 …

1045 Q&T, 390 HB 200 29 1274 184.8 1343 194.8 … … 0.04 59 1860 269.8 0.89

1045 Q&T, 500 HB 200 29 1728 250.6 1956 283.7 2351 341.0 0.04 38 2306 334.4 …

1045 Q&T, 705 HB 200 29 1825 264.7 2067 299.8 … … 0.19 2 2135 309.6 0.02

10B21 Q&T, 320 HB 200 29 999 144.9 1048 152.0 1294 187.7 0.05 67 1499 217.4 1.13

1080 Q&T, 421 HB 207 30 978 141.8 1349 195.6 2227 323.0 0.15 32 1645 238.6 …

4340 Q&T, 350 HB 200 29 1178 170.8 1240 179.8 1580 229.2 0.07 57 1653 239.7 0.84

4340 Q&T, 410 HB 207 30 1371 198.8 1467 212.8 … … … 38 1557 225.8 0.48

5160 Q&T, 440 HB 207 30 1487 215.7 1586 230.0 1940 281.4 0.05 39 1931 280.0 0.51

8630 Q&T, 254 HB 207 30 709 102.8 785 113.9 1061 153.9 0.08 16 840 121.8 0.17

Cyclic yield

strength

(S′

)

Cyclic

strength

exponent

(K′)

Cyclic true

fracture

stress (σ′

)

Alloy Condition

(a)

MPa

ksi MPa

ksi

Cyclic

strain

hardening

exponent

(n′)

MPa ksi

b Cyclic

true

fracture

strain(ε′

)

Cyclic properties

(c)

A136 As-received 330 47.9 1026 148.8

0.18 799 115.9 -

0.09

0.22

0.46

A136 150 HB 337 48.9 1151 167.0

0.2 846 122.7 -

0.08

0.20

0.42

SAE950X

As-received,

137 HB

353 51.2 957 138.8

0.16 772 112.0 -

0.08

0.34

0.52

SAE950X

As-received, 409 59.3 939 136.2

0.13 824 119.5 -0.42