关键词:J积分;塑性断裂;半解析公式;能量等效假设;I型裂纹 Abstract The J-integral to characterize the singular level of the stress and strain field at the crack tip is definite and rigorous and is a basic parameter of elastoplastic fracture mechanics. The calculation of J-integral mainly depends on the plastic factor method and the finite element method at present. For theoretical predicting and testing of material fracture toughness, it is important and difficult to obtain analytical expressions about J-integral-load and load-displacement relations of cracked components. The most widely used test for structure integrity evaluation with J-integral is the ductile fracture toughness of type-I cracked specimens. Here, based on the Chen-Cai energy equivalence hypothesis, a unified characterization method of J-integral-load and load-displacement relation is proposed for six Mode-I cracked components which are commonly used in fracture toughness test under the plane strain condition. Then, the undetermined parameters of the engineering semi-analytical formulas of the J-integral-load and the load-displacement relations are obtained by a small amount of finite element analysis. The results show that the J-integral-load and load-displacement relation predicted by the unified semi-analytical formulas are in good agreement with those from finite element method. The engineering semi-analytical J-integral-load formula, which contains the elastic modulus, stress strength coefficient and strain hardening exponent of materials, can be widely adapted for different materials. And the J-integral value corresponding to arbitrary load points can be easily obtained by the formula. The presented novel method is convenient to establish the engineering semi-analytical formulas of J-integral-load and load-displacement relations for various type-I cracked components or specimens.
显示原图|下载原图ZIP|生成PPT 图5预测与计算的CT全塑性载荷-位移曲线比较 -->Fig. 5Comparison of fully plastic load-displacement curves predicted by formula and those from FEA for CT specimen -->
同理,本文还得到了SEB和SENT等其他5种试样 积分统一公式的未知参数,表2给出了其参数数值,图6给出了SEB、SENT等试样 载荷位移曲线公式预测与有限元结果对比,图7给出了各试样构元在 MPa 2 000 MPa, 时统一公式对J积分的预测结果与有限元对比. Table 2 表 2 表 2各类裂纹构元的J积分统一公式参数 Table 2Unified formula parameters of J-integral for various cracked components
新窗口打开 显示原图|下载原图ZIP|生成PPT 图6式(19)预测的弹塑性条件下载荷位移曲线与有限元比较 -->Fig.6Comparison of elastoplastic load-displacement curves predicted by Eq.(19) with those from FEA -->
显示原图|下载原图ZIP|生成PPT 图7式(23)预测的J积分与有限元结果比较 -->Fig. 7Comparison of J-integral predicted by Eq.(23) with those from FEA -->
3 结 论
(1) 基于Chen-Cai能量等效假设,结合 积分能量定义式,提出了一种解析求解I型裂纹构元 积分的方法, 这种新方法 旨在针对一系列I型裂纹标准试样和非标准试样可以较易实现获得 积分半解析的表达式,以便用于测试和断裂问题的理性分析. (2)对于6种I型裂纹构元,通过有限元的计算给出了 积分-载荷和载荷-位移统一公式的参数;依靠 积分统一公式预测的 积分结果相较有限元结果都吻合较好. The authors have declared that no competing interests exist.
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