Posted on Categories:Fracture mechanics, 断裂力学, 物理代写

# 物理代写|断裂力学代写Fracture mechanics代考|ENGR7891 The R-curve

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## 物理代写|断裂力学代写Fracture mechanics代考|The R-curve

The graphical representation of the energy criterion is known as R-curve, whose construction procedure is as follows. The $G$ and $R$ values are plotted in the vertical axis, and the crack length is plotted in the horizontal axis, where the initial crack size $\left(a_1\right)$ is plotted to the left and the crack extension ( $\Delta$ a) to the right. The $G, R$ axis intersects the crack size axis at $\Delta a=0$. As mentioned in the previous section, in plane stress condition,
$$G=\frac{K^2}{E}$$
For an infinite plate with a central crack under plane stress, the stress intensity factor is $K_I=\sigma \sqrt{ }(\pi a)$; therefore, $G$ becomes
$$G=\frac{\pi \sigma^2 a}{E}$$
Plotting the above equation on the R-curve shows that the variation of $G$ is a straight line with a slope equal to $\pi \sigma^2 / E$. If $R$ is constant and independent from the crack size, its plot is a horizontal straight line. The resulting R-curve is schematically shown in Fig. 3.4.

## 物理代写|断裂力学代写Fracture mechanics代考|Plane strain fracture toughness

It has been experimentally observed that fracture toughness $\left(K_C\right)$ varies with the thickness, as schematically shown in Fig. 3.7. The most important feature of this behavior is that $K_C$ is constant for thick specimens in plain strain condition, thus $K_C$ becomes material property identified as plane strain fracture toughness, represented by the symbol $K_{I C}$, since it is determined in crack opening Mode I. It is relevant to remark that the plane strain $K_{I C}$ is also the minimum value of $K_C$ with respect to the thickness, while the maximum $K_C$ occurs under plane stress and plane strain combinations. Although the exact cause for such behavior is not clear yet, it is likely to be due to the plasticity effects combined with the plastic zone size and shape, since these characteristics induce more energy consumption at the onset of instability and crack propagation.

Irwin introduced an expression to calculate the plane stress fracture toughness based on the plane strain fracture toughness that has the following form:
$$K c=K_{I C}\left[1+\frac{1.4}{B^2}\left(\frac{K_{I C}}{\sigma_0}\right)^4\right]^{0.5}$$

Furthermore, it has been experimentally found that the plane strain condition occurs at thicknesses $(B)$ that meet the condition:
$$B>2.5 K_{I C}^2 / \sigma_0$$

## 物理代写|断裂力学代写骨折力学代考| r曲线

. r曲线 .物理代写|

$$G=\frac{K^2}{E}$$

$$G=\frac{\pi \sigma^2 a}{E}$$

## 物理代写|断裂力学代写断裂力学代考|平面应变断裂韧性

Irwin引入了基于平面应变断裂韧性计算平面应力断裂韧性的表达式，其形式如下:
$$K c=K_{I C}\left[1+\frac{1.4}{B^2}\left(\frac{K_{I C}}{\sigma_0}\right)^4\right]^{0.5}$$

$$B>2.5 K_{I C}^2 / \sigma_0$$

## MATLAB代写

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