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Method for determining Jz integral of three-dimensional elastic-plastic bending crack tip under action of impact load
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A bending crack and crack tip technology, which is applied in the field of determining the JZ integral of the three-dimensional elastic-plastic bending crack tip, can solve problems that have not yet been studied, two-dimensional linear elastic fracture, two-dimensional elastic-plastic fracture, etc.
Pending Publication Date: 2019-11-22
ZHENGZHOU TECHN COLLEGE
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[0002] The crack characteristics of the three-dimensional cracked body are an important factor affecting the service life of the three-dimensional cracked body. The research on the crack characteristics of the three-dimensional cracked body can more accurately understand the damage of the three-dimensional cracked body. The main parameters for evaluation, but the current research results on the bending crack propagation path are limited to two-dimensional linear elastic fracture and two-dimensional elastic-plastic fracture problems, about the three-dimensional elastic-plastic bending crack dynamic J Z The determination of the integral has not been studied so far;
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Embodiment 1
[0195] Embodiment one: see Figure 1-5 , when the crack body is aluminum alloy, the dynamic J for the three-dimensional bending crack tip Z Integral calculation and analysis, Poisson's ratio of aluminum alloy ν = 0.33, σ s =325MPa, E=0.72×10 11 Pa,D=6500s -1 ,P=4,K d1 =3.36,
[0196] When the impact load applied to the cracked body is: σ aZ (t) = 0.025σ s (t 2 +3t-20), t∈[0,5],σ rZ (t) = 0.02σ s When t, t∈[0,5], it can be obtained from the above formula (27):
[0197]
[0198]
[0199]
[0200] Then, according to formulas (34), (35), (36), (37), (38), (39), and (40), the three-dimensional elastic-plastic bending crack tip dynamic J at t=3 seconds can be calculated Z integral maximum;
Embodiment 2
[0201] Embodiment two: see Figure 6-10 , when the crack body is titanium 50A, the dynamic J for the three-dimensional curved crack tip Z Integral calculation and analysis, the Poisson's ratio of titanium 50A ν = 0.34, σ S =621MPa, E=1.16×10 11 Pa, D=120s -1 ,P=9,K d2 =6.35,
[0202] When the impact load applied to the cracked body is: σ aZ (t) = 2.64σ S e t-8 / t, t∈[0,8], When t∈[0,8], it can still be obtained from formula (41):
[0203]
[0204] Furthermore, the three-dimensional elastic-plastic bending crack tip dynamic J at t=8 seconds can be calculated Z integral maximum;
[0205] From the analysis of Example 1 and Example 2, it can be seen that under the same impact load, the dynamic J Z The integral decreases as the thickness of the 3D crack body increases; when the thickness of the 3D crack body increases uniformly, the dynamic J of the 3D curved crack tip Z The integral keeps decreasing, and the reduction is getting smaller and smaller.
Embodiment 3
[0206] Embodiment three, see Figure 11-15 , it can be analyzed that under the same impact load, the thickness of the three-dimensional crack body gradually increases. For the same length of the straight line part of the crack and the same bending degree, the dynamic J Z The speed at which the integral increases gradually decreases with increasing impact load. When the thickness of the 3D crack body increases uniformly, the dynamic J of the 3D curved crack tip Z The speed at which the integral increases as the impact load increases gradually decreases. In addition, it can be seen that when the thickness of the three-dimensional crack body is the same, the dynamic J of the three-dimensional bending crack tip Z The integral increases with the continuous increase of the impact load;
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Abstract
The invention discloses a method for determining the JZ integral of a three-dimensional elastic-plastic bending crack tip under the action of an impact load, and the method comprises the steps: calculating the dynamic JZ integral of the three-dimensional elastic-plastic bending crack tip through a second-order perturbation method and the comprehensive consideration of the impact stress and the dynamic normal stress and dynamic shearing stress at the boundary of a three-dimensional plastic region; calculating a dynamic JZ integral of the three-dimensional elastic-plastic bending crack tip by using a numerical solution, and drawing a graph to analyze a change relationship between the dynamic JZ integral of the three-dimensional elastic-plastic bending crack tip and the geometric dimension ofa three-dimensional crack body, wherein the obtained dynamic JZ integral of the three-dimensional elastic-plastic bending crack tip is reduced along with the increase of the thickness of a three-dimensional crack body, the reduction amplitude is smaller and smaller, and finally, the dynamic JZ integral of the elastic-plastic bending crack tip tends to be in a plane strain state; when the sizes ofthe three-dimensional crack bodies are the same, the conclusion that the dynamic JZ integral of the tip of the three-dimensional bent crack is increased along with the continuous increase of the external impact load is of great significance to the safety evaluation of the three-dimensional crack bodies in the fields of ships, aviation and engineering.
Description
technical field [0001] The present invention relates to the research and analysis of the expansion path of bending cracks, in particular to the three-dimensional elastoplastic bending crack tip J under the action of impact load Z How to determine points. Background technique [0002] The crack characteristics of the three-dimensional cracked body are an important factor affecting the service life of the three-dimensional cracked body. The research on the crack characteristics of the three-dimensional cracked body can more accurately understand the damage of the three-dimensional cracked body. The main parameters for evaluation, but the current research results on the bending crack propagation path are limited to two-dimensional linear elastic fracture and two-dimensional elastic-plastic fracture problems, about the three-dimensional elastic-plastic bending crack dynamic J Z The determination of the integral has not been studied so far; [0003] In engineering practice, the...
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