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|ENME667 Stress concentration

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## 物理代写|断裂力学代写Fracture mechanics代考|Stress concentration

According to the definition of stress, a reduction in the cross-section area means an increment of the stress, in an amount proportional to the magnitude of the area reduction. However, the sharp changes of crosssection, as well as discontinuities, such as holes, grooves, gouges, etcetera, increase the stress beyond the magnitude given by the sole reduction of the cross-section area. This phenomenon is called stress concentration and is of great technological importance, because it increases the local stress above nominal applied stresses. The magnitude of the stress increment due to the stress concentration is called stress concentration factor, defined by the symbol $K_T$, therefore
$$K_T=\frac{\sigma_{\max }}{\sigma_{a p p}}$$
Where $\sigma_{\max }$ is the maximum stress value at the root of the stress concentrator, and $\sigma_{a p p}$ is the applied stress. One of the first stress concentration factors was obtained by Inglis in 1913 , for an infinite thin panel with an elliptic hole in the center. The expression for $K_T$ is
$$K_T=1+2\left(\frac{a}{b}\right)$$

## 物理代写|断裂力学代写Fracture mechanics代考|Definitions and basic concepts of fracture

Fracture is defined as the separation or fragmentation of a solid under the action of stresses through a process of creation of new surfaces that are the fracture surfaces. Normally, to fracture a material after yielding, it is necessary to increase the stress until a crack nucleation mechanism takes place, followed by crack growth and final separation. Depending on the load conditions, body geometry and the mechanical properties of the material, it may be necessary to increase the load after the crack initiation has started to further cause fracture, whereas in other cases, it will be sufficient to reach the point of crack initiation to have the crack to growing spontaneously. A very important circumstance is that the fracture can initiate from a preexisting crack or a severe stress concentrator, so the nucleation stage is suppressed, and the fracture process consists only of the crack propagation and final separation stages.

It is important to point out that in order to break a solid component, it is not necessary that the initiation and crack propagation conditions be present throughout the entire body’s volume, but since the fracture process occurs on a plane, it is enough to meet the fracture conditions in that single plane. This is similar to the chain principle that says, “To break a chain, it is enough to break a single link.” The fact that a fracture may initiate on a localized plane, or more precisely in a narrow region, where there may be stress concentrators or preexisting flaws, suggests that it may take place at stresses lower than the design stresses, all of this provide the fracture characteristics of being sudden, unexpected and, very often, catastrophic.

Depending on the amount of plastic strain before failure, two types of fractures are recognized, as shown in Fig. 1.16.

Brittle fracture: The strain in most of the body’s volume is elastic and the extent of plastic strain is negligible; so, if after the fracture the fragments are reassembled, the component will have the same initial geometry.

Ductile fracture: It is the fracture after an appreciable amount of plastic strain in most of the body’s volume and consequently, there is a permanent change of geometry. In components under tensile stresses, the plastic deformation close to the fracture surface will show a lateral contraction called neck.

Quasibrittle fracture: The plastic deformation zone is concentrated close to the fracture surface, so the fracture component displays a brittle appearance, but the fracture mechanism is essentially ductile.

## 物理代写|断裂力学代写骨折力学代考|应力集中

$$K_T=\frac{\sigma_{\max }}{\sigma_{a p p}}$$

$$K_T=1+2\left(\frac{a}{b}\right)$$

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