PSI - Issue 51

Yu.G. Matvienko et al. / Procedia Structural Integrity 51 (2023) 76–80 Yu.G. Matvienko / Structural Integrity Procedia 00 (2022) 000–000

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the constraint parameter A describes the crack-tip stress, the J-A fracture criterion (2) can be interpreted as follows: fracture in a structural element and in experimental specimen occurs at the same crack-tip stress field. 3. The two-parameter J-A fracture criterion A two-parameter elastic-plastic fracture criterion is based on the relationship between the J -integral and strains/stresses on the surface of the crack/notch as well as the principle of linear summation of damage and presented in the following form by Matvienko and Morozov (2004) � ��� ����� � / � � � � �� � � , (3) where ����� � � � � � � , � is the ultimate tensile strength, � is the true ultimate strength, � is the applied failure stress, n is the strain hardening exponent in the Ramberg–Osgood power-law. Here, ��� is the fracture toughness of the material which is measured under conditions of maximum crack-tip constraint; J is the applied J -integral at the crack tip. To reflect crack-tip constraint, the constraint parameter A as a function of the applied failure stress � should be introduced in the criterion (3). According to Ding and Wang (2012), the following useful equation can be employed � � � � � � � ���������� , (4) where � is the limit stress for a given crack configuration. In contrast to Ding and Wang (2012), the coefficient � for failure conditions of the body should be a function of geometry of the body, the crack aspect ratio, the strain hardening exponent as well as the applied failure stress � and should be calculated from Eq. (4). Moreover, the parameter in Eq. (4) is a function both crack length and the applied stress. Combining Eqs. (3) and (4) for failure conditions, the quantitative two-parameter elastic-plastic J-A criterion and the constraint corrected fracture toughness �� �� can be represented as follows � �| � � �� �� � ��� ���� � � � � ����������� � � � � � � � � �� � � . (5) Here it is taken into account that the contribution of the term � � / � � � to the right-hand side of the fracture criterion (3) is negligible and λ → 1 for the extensively used structural metals with the strain hardening exponent n ≥3 and � / � �� . 4. Results and discussion To estimate the constraint corrected fracture toughness , some parameters and mechanical properties of the material should be employed. In this paper, the effect of some parameters and mechanical properties on the normalized constraint corrected fracture toughness is illustrated for single edge cracked plate ( ECP) with varying crack aspect ratios, the applied stress ratio and the strain hardening exponent. The values of constraint parameter A , asymptotic powers s and t are listed in tables by Ding and Wang (2010). Limit loads for rigid-plastic bodies are used according to Anderson (2005) for normalizing the applied stresses � � �.��� � � � �������� � � �� � � �, (6) where � is the yield stress, a is crack length, W is specimen width. Limit loads for this specimen are given in the form of remote stress. The values of coefficient a 1 are calculated by means of Eq. (4) as the following function � � � � � / � � . The ratio of the yield stress � to the ultimate tensile strength � is assumed to be 0.7 for many