PSI - Issue 39

Abhishek Tiwari / Procedia Structural Integrity 39 (2022) 290–300 Author name / Structural Integrity Procedia 00 (2019) 000–000

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relation analogous to Eq. (2-3). The CF-concept has enabled the evaluation of the driving force of stationary and growing cracks in elastic−plastic materials and materials with eigen -strains. The crack driving force (CDF) vector is calculated by summing the bulk configurational forces in a contour. For a homogeneous material, the value of the CDF, which is identical to the conventional J -integral for elastic materials, is path independent as long as the deformed zone remains inside the contour. For elastic materials, the CDF calculated using configurational forces should cover a small zone at the crack tip as there are some configuration forces due to the discretization error (Kolednik et al. 2014). For contours outside the deformed zone for elastic+plastic or elastic+creep cases, and outside of the discretization zone for elastic cases, the value of the contour integral will be independent of the contour. This path independence gives an advantage to measure the CDF at a farther location from the crack tip. However, in presence of a transition of material’s mechanical response in reference configuration, this path independence disappears. 2. Material inhomogeneity effect: Calculation of crack driving force The configurational forces arise in a continuum space in presence of a defect. The defect is anything which has a different mechanical property in the reference configuration. A change in material property can be created deliberately to use the effect of the material inhomogeneity for better crack resistance of materials. Defects in a material exist at every scale and their effect also changes with the scale or magnitude of the observation. For instance, an interstitial can also result in a configurational force, however, the scale we are looking at is of the concern to fracture mechanics and at this scale defects like a hole, or a gradual or sudden transition of material’s mechanical properties can result in a configurational force which will influence the crack driving force. This can be visualized in Fig. 1, a cracked specimen with an interface is shown where across interface the mechanical property takes a sharp jump. Due to this change in mechanical property additional configurational forces arise on the interface and hence the path independence of the J -integral disappears. Similar phenomena can happen when the material transition is not very sharp along an interface but gradual. For instance, along a dissimilar metal weld or along an interlayer where the material transition can happen at two different interfaces and even in these cases the influence of the configuration forces on crack driving force will be significant. Under the situation where the material transition occurs, the contour integral value for different contours will be different because there will be more than one defect in the contour… one would be the crack tip and another would be the interface where the sudden or gradual transition occurs. In presence of an interface, Σ, where a sudden change in the mechanical property occurs, configurational forces arise at the interface which can be expressed as in Eq. (5), = ( ⟦ ⟧ − ⟦ ⟧〈 〉 ) , (5) where, ⟦ ⟧ , represents the jump in the parameter from left to right of the interface and 〈 〉 represents the average value of the left and right side values of the parameter. From the previous studies on effect of interfaces on the crack driving forces by Simha et al. (2005) and Simha et al. (2008), the behavior of crack driving force is known in presence of a sharp interface at 90 o from the crack plane. Recently, the influence of interfaces at various orientation has also been studied by Tiwari (2021). The J tip / J far ratio increases as a crack tip moves closer to the interface between a stiff and a compliant material resulting in a crack tip anti-shielding effect or in simple words it can be said that the crack is attracted towards this interface and opposite is true for a compliant to stiff transition of crack tip.

3. Crack driving force under creep deformation As discussed earlier that the crack driving force under creep deformation can be calculated by treating the creep strain as the eigen-strain and the value of the conventional J-integral is calculated by summing up the configurational forces inside the contour will be dependent on time and therefore the rate of change of crack driving force can be