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

77

2

crack tip is controlled by two parameters of fracture mechanics, namely, the J -integral and the parameter A . The parameter A is a measure of the deviation of the stress field from the HRR-stress field and can be considered as a parameter of elastic-plastic constraint at the crack tip both under conditions of small scale yielding and large scale yielding. Similar approach ( J-A 2 approach) was developed by Yang et al. (1993). The difference of these solutions is just in distance scaling. The two-parameter J-A fracture criterion should be based on comparing the J -integral � � �| � � of a structural element containing a crack with the experimentally measured fracture toughness J C corresponding to computed value of the constraint parameter A as it was proposed by Matvienko and Nikishkov (2017).

Nomenclature A J J -integral �� ��

crack-tip constraint parameter

constraint corrected elastic-plastic fracture toughness n strain hardening exponent � limit stress � ultimate tensile strength � yield stress 2. Theoretical background of the J-A concept The three-term asymptotic solution for elastic-plastic crack-tip stresses in the following form � �� � � � � � � � � � �� � � � � � � � � �� � �� � � � � ���� � � � � �� � � (1) Here, A is the second fracture parameter; �� are stress components �� , �� and �� in the polar coordinate system rθ with origin at the crack tip; � � � � �� are dimensionless angular stress functions, � � �� �� � �� . Power t is an eigenvalue that depends on the hardening exponent n . The coefficient A 0 is introduced as � ���� � � � � . The parameter I n is a scaling integral depending on the hardening exponent. Dimensionless radius is defined by the following formula � � � � � . It should be noted that the three terms of expansion (1) are controlled by two parameters: the traditional elastic plastic fracture mechanics parameter, namely, J -integral and the additional parameter A . The first term of the asymptotic expansion (1) is exactly the HRR solution of elastic-plastic stresses in the vicinity of the crack tip. The parameter A is a measure of stress field deviation from the HRR stress field and can be considered as a crack-tip constraint parameter. It was also shown that the J-A stress field is much closer to elastic-plastic finite element results than the HRR stress field as it was shown by Nikishkov and Matvienko (2016). Moreover, it was also shown that there is the combination effect of the crack aspect ratio and specimen thickness on the constraint parameter A . It means that in-plane and out-of-plane constraint effects show significant interaction and affect the parameter A . The two-parameter J-A fracture criterion is based on comparing the J -integral of a structural element containing a crack with the experimentally measured fracture toughness corresponding to computed value of the constraint parameter A as it was formulated by Matvienko and Nikishkov (2017) � �| � � � � � (2) The value of J -integral is computed for a structural element under load P using some well-known approaches. After that the constraint parameter A is estimated using the finite element stress data and the asymptotic expansion (1) according to the procedure, the details of which are given by Nikishkov and Matvienko (2016). The computed J -integral should be compared with the experimental fracture toughness J C that is measured using a test specimen with same value of A . Since the three-term asymptotic solution as a combination of the J- integral and