**Figure 9.**

bushings generally exhibit the characteristics of ductile materials and alloy steels

properties of **Table 1** were used to evaluate the durability of the precise cylinder block. **Figure 7** shows the result of the measurement, not the literature, and the

The residual stress acts as a mean stress at the time of durability assessment, and safety is different as shown in **Figures 8** and **9**. Therefore, in **Figure 9**, the result of **Table** 1 will be used to draw the Haigh diagram baseline clearly.

> <sup>2</sup> mean stress

In addition to the Haigh diagram, there are five other diagrams to easily assess the durability of a product and to illustrate it. The expressions for expressing diagrams are the same as **Table 2**. Goodman, Gerber, SAE, Soderberg and Modified Goodman shown in **Table 2** are shown in **Figure 10**. As you can see in **Figure 10**, Soderberg, Modified Goodman, SAE, Goodman and Gerber are listed in the most conservative order of product evaluation for durability. The most similar form to

<sup>2</sup> ð Þ alternating stress (1)

**Alloy steel Copper alloy steel**

(2)

exhibit characteristics of brittle materials [5]. The results of the material

*New Challenges in Residual Stress Measurements and Evaluation*

*<sup>σ</sup><sup>a</sup>* <sup>¼</sup> *<sup>σ</sup>max* � *<sup>σ</sup>min*

<sup>σ</sup><sup>m</sup> <sup>¼</sup> <sup>σ</sup>max <sup>þ</sup> <sup>σ</sup>min

The Haigh diagram (**Figure 11**) can be accurately draw as following:

Tensile strength 194 226 Yield strength 100 161 Elongation (%) 25 5.45

Point 1: The right limit of the Haigh diagram is generally given by the tensile

Points 2 and 3: For ductile materials, the second point is defined as the intersection between the straight line σ<sup>o</sup> = σ<sup>y</sup> and the straight line through the alternating stress limit of the material (σA,tsc,R= �1) and its pulsating stress limit (σA,tsc, R = 0).

confirmed values are shown in **Table 1**.

Haigh diagram is Modified Goodman.

strength of the material.

**Table 1.**

**Figure 8.**

**130**

*Important of residual stress.*

*Value of test results.*

*Important of material property.*

Point 3 is identical with point 2. For GG the points 2 and 3 are, as a result of experiments, defined as:

Point 2: σ<sup>m</sup> = 0.88�σUTS, σ<sup>0</sup> = 0.34�σA,tsc and.

Point 3: σ<sup>m</sup> = 0.76�σUTS, σ<sup>a</sup> = 0.48�σA,tsc.

Point 4: Pulsating stress limit (amplitude) of the material.

Point 5: Alternating stress limit of the material under tension/compression.

Point 6: For ductile materials, point 6 is defined as the intersection of the straight line σ<sup>1</sup> = � σ<sup>y</sup> with the lengthening of the straight line from point 4 to point 5. For GG an average inclination of the straight line of 30 degree is derived from known compression pulsating stress limits, which, together with a straight line R = �∞, give point 6. If the compression pulsating stress limit of the material is known, point 6 can be derived from it.

Point 7: For GG, point 7 is determined by half of the length of an orthogonal straight line through the intersection of the compression-fracture border line with the straight line R = �∞. For all other materials, point 7 is identical with point 6.

Point 8: It is the intersection of a horizontal straight line through point 6 with the straight line σ<sup>l</sup> = σc,C.


*Subscript notation: a = alternating, y = static tensile yield, m = mean, u = static tensile ultimate, e = modified material constant, β = Se(Su* � *Sy)/Su(Sy* � *Se), σ<sup>a</sup>* ¼ alternating stress in enviroment condition*,*

*σ<sup>m</sup>* ¼ mean stress in enviroment condition*, Se* ¼ modified stress of material*,*

*Sf* ¼ fatigue limit of material in environment condition*, Sy* ¼ yield stress of material*,*

*Su* ¼ ultimate stress of material*.*

**Table 2.** *Types of HAIGH Diagram.*

σ<sup>a</sup> and Se necessary for drawing the Haigh diagram as shown in **Figure 12**. In order to consider the fatigue factor, more complicated calculations must be accompanied. Therefore, it is recommended to use the fatigue program for efficient and accurate

The purpose of this study is to quantitatively predict the residual stresses that are necessary before actual cylinder block for use. Therefore, it is important to set up an appropriate method of simulation, which is an economic evaluation method, before production. For this purpose, this study compares the surface pressure distribution of the simulation with the surface pressure prediction calculated as

*Es*

which is obtained by setting the following stress conditions (**Figure 14** and

*dr* , *εθ* <sup>¼</sup> *<sup>u</sup>*

*r*

*<sup>a</sup>*2þ*b*<sup>2</sup> *b*2 �*a*<sup>2</sup> � *<sup>ν</sup><sup>s</sup>*

*Face Pressure* (3)

*<sup>r</sup>* <sup>¼</sup> <sup>0</sup> *Equilibrium Equation* (4)

*Strain* (5)

fatigue safety factor evaluation.

*Change curved because of fatigue parameter.*

*Durability Assessment Considering Residual Stress DOI: http://dx.doi.org/10.5772/intechopen.90298*

**Figure 12.**

(**Figure 13** and Eq. 3) [6].

*ν<sup>h</sup>* ¼ Poisson<sup>0</sup>

*ν<sup>s</sup>* ¼ Poisson<sup>0</sup>

Eqs. (4) and (5)).

*σ<sup>r</sup>* ¼ radial stress, *σ<sup>θ</sup>* ¼ tangential stress, *ε<sup>r</sup>* ¼ radial strain, *εθ* ¼ tangential strain,

**133**

**3.3 Verification of simulation method**

<sup>p</sup> <sup>¼</sup> *<sup>δ</sup>*

*Eh* ¼ modulus of elasticity for hole material,

s ratio for hole material, *Es* ¼ modulus of elasticity for shrink material,

s ratio for shrink material

*dr* <sup>þ</sup> *<sup>σ</sup><sup>r</sup>* � *σθ*

*<sup>ε</sup><sup>r</sup>* <sup>¼</sup> *du*

*b Eh b*2 þ*c*<sup>2</sup> *<sup>c</sup>*2�*b*<sup>2</sup> <sup>þ</sup> *<sup>ν</sup><sup>h</sup>* <sup>þ</sup> *<sup>b</sup>*

*dσ<sup>r</sup>*

*u* ¼ displacement of radial direction

**Figure 10.** *Fatigue lines to various fracture theories. (a) Fracture theory, and (b) Yield theory.*

Point 9: The left limit of the Haigh diagram is given by the ultimate stress limit under compression of the material.

However, the S-N curve and the S-S curve can be changed by the size effect, the relative stress gradient, and the temperature effect, which are exactly the values of

*Durability Assessment Considering Residual Stress DOI: http://dx.doi.org/10.5772/intechopen.90298*

**Figure 12.** *Change curved because of fatigue parameter.*

σ<sup>a</sup> and Se necessary for drawing the Haigh diagram as shown in **Figure 12**. In order to consider the fatigue factor, more complicated calculations must be accompanied. Therefore, it is recommended to use the fatigue program for efficient and accurate fatigue safety factor evaluation.
