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Numerical Analysis of Constraint Effect on Crack-Tip and Its Application

Author: ZengZhen
Tutor: ChenZhongAn
School: Jiangsu University
Course: Solid Mechanics
Keywords: HRR theory J-A2 three-term solution three-point bending (TPB) specimen constraint RKR cleavage model fracture toughness ductile-brittle transition curve (DBT curve) A2 parameter Weibull stress Master curve
CLC: O346.12
Type: Master's thesis
Year: 2006
Downloads: 166
Quote: 3
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Abstract


The geometry and loading mode have a prominent effect on toughness of specimens. Initially, the HRR field theory developed by Hutchinson, Rice and Rosengren is been introduced. Basing on HRR theory, the J-A2 theory, which is the theory background of paper, proposed by Yang and Chao is been referred to in our word following. The analysis completed by finite element method indicates that the constraint level had a prominent effect on crack-tip stress field. This phenomenon can be attributed to the constraint effect. The comparison of HRR solution, J-A2 three-term solution and finite results indicates that HRR solution is only suitable for characterizing crack-tip stress fields of deep-crack specimens and J-A2 methodology is sufficient to characterize the crack-tip fields for various crack geometry.Making use of J-A2 three-term solution characterizing the crack-tip stress field of elastic-plastic material combining with RKR cleavage model, three equations are given by matching the different crack-tip fields. The three correlations are: （1） the correlation between yield stresses of the high constraint and low constraint specimens when they are failure at different temperature but at the same toughness; （2） the correlation between the two toughness when two specimens are failure at the same temperature; （3） the equation to evaluate the full DBT curve in the condition that the two parameters in RKR model are specified. The procedure to predict the DBT curve is given in detail: 1. analylize the parameter A2 of non-standard specimens and specify its value; 2. calculate two necessary parameter in RKR model; 3. substitute this A2 value and two parameter in RKR model into correlation （1）, （2） and （3）. Then, the finite element analysis code ABAQUS is performed to determine A2 for two TBP specimens made of A533B steel （a/W=0.075 and a/W=0.5）. The analysis for A2 value shows that A2 is not only independent of loading but also independent of temperature over ductile-brittle transition range. Therefore, constraint parameter A2 is recognized as a constant in our paper. According to the procedure, the ductile-brittle transition （DBT） curve of a/W=0.075 specimens can be obtained from the fitted line of a/W=0.5 toughness. These curves are consistent with test data and the results suggest that the procedure proposed in this work is valid.The toughness obtained from one material under the same temperature shows a statistical distribution. Basing on this reality, the similar procedure basing on cumulative probability fracture （Weibull stress model） is included in last section of paper. The median toughness curve （master curve） of a/W=0.5 is analyzed and the corresponding prediction

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CLC: > Mathematical sciences and chemical > Mechanics > Solid Mechanics > Strength theory > Fracture theory > Ductile fracture
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