**3.2 Material property check**

The shape and material have a great influence on the residual stress as well as the rate of shrink fit when the copper bushing is pressed into the cylinder block. In order to predict the accurate residual stress, a characteristic test was performed on the material except for the shape selected through the design [4]. The reason for this is that, in the case of metallic materials, the material properties such as yield stress and tensile stress vary depending on the production method of the material. Therefore, in order to perform accurate durability assessment, the abovementioned yield stress and tensile stress value should be basically confirmed. The test results of yield stress and tensile stress are shown in **Figure 7** and **Table 1**. Experimental results were derived from other common aspects that copper

**Figure 7.** *Material property test results.*

bushings generally exhibit the characteristics of ductile materials and alloy steels exhibit characteristics of brittle materials [5]. The results of the material 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 confirmed values are shown in **Table 1**.

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.

$$
\sigma\_a = \frac{\sigma\_{\text{max}} - \sigma\_{\text{min}}}{2} (\text{alternating stress}) \tag{1}
$$

$$
\sigma\_{\rm m} = \left(\frac{\sigma\_{\rm max} + \sigma\_{\rm min}}{2} \,\text{mean stress}\right) \tag{2}
$$

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

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

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

**Fracture theory Goodman Gerber SAE**

**Yield theory Soderberg Modified Goodman**

*Su* ¼ 1 *<sup>σ</sup><sup>a</sup>*

*Sy* ¼ 1 *<sup>σ</sup><sup>a</sup>*

*Subscript notation: a = alternating, y = static tensile yield, m = mean, u = static tensile ultimate, e = modified material*

*Se* <sup>þ</sup> *<sup>σ</sup><sup>m</sup> Su* <sup>2</sup> ¼ 1

*Se* <sup>þ</sup> *<sup>σ</sup><sup>m</sup>*

*σa*þ*σ<sup>m</sup>*

*Su* <sup>¼</sup> <sup>1</sup> *for <sup>σ</sup><sup>a</sup>*

*Sy* <sup>¼</sup> <sup>1</sup> *for <sup>σ</sup><sup>a</sup>*

*σa se* <sup>þ</sup> *<sup>σ</sup><sup>m</sup> Sf* ¼ 1

*<sup>σ</sup><sup>m</sup>* ≥*β* 

*<sup>σ</sup><sup>m</sup>* ≤*β* 

*Se* <sup>þ</sup> *<sup>σ</sup><sup>m</sup>*

*Se* <sup>þ</sup> *<sup>σ</sup><sup>m</sup>*

*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*,*

experiments, defined as:

*Important of material property.*

**Figure 9.**

6 can be derived from it.

straight line σ<sup>l</sup> = σc,C.

Equation *<sup>σ</sup><sup>a</sup>*

Equation *<sup>σ</sup><sup>a</sup>*

*Su* ¼ ultimate stress of material*.*

*Types of HAIGH Diagram.*

**Table 2.**

**131**

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.

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

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

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 Haigh diagram is Modified Goodman.

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

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

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).


#### **Table 1.**

*Value of test results.*

**Figure 8.** *Important of residual stress.*
