Study On Unified Parameter Of In-plane And Out-of-plane Creep Constraint Based On Crack-tip Equivalent Creep Strain

As crack-tip constraint can dramatically affect creep crack growth(CCG)behavior of materials and structures.To accurately predict the creep life and achieve structural integrity assessments for high temperature components,it is necessary to take the creep crack-tip constraint effect into consideration.Constraints can be divided into in-plane constraint and out-of-plane constraint.For the three dimensional cracks in actual high-temperature components,both in-plane and out-of-plane constraints exist simultaneously.They can be affected by crack depth,length of the un-cracked ligament,loading configuration and thickness of specimens and structures.In order to accurately incorporate creep crack-tip constraint effect in creep life assessments of high-temperature components with cracks,a unified constraint parameter which can characterize both constraints together is required.In this paper,by using the combined methods of the finite element simulations,creep test data and theretical analysis,a unified creep constraint parameter Ac has been defined based on the area surrounded by the crack-tip equivalent creep strain isoline and the relationship between creep crack growth rate and the parameter Ac has been established.Based on the unified creep constraint parameter Ac,the constraint level of welded joint C(T)specimens has been calculated and analyzed.The creep constraint and constraint parameter solutions for inner axial and circumferential semi-elliptical surface cracks in pressurized pipes has been investigated.The main work and results are summarized as follows:(1)The creep crack growth(CCG)rates of specimens with different in-plane and out-of-plane constraints were simulated over a wide range of C*by using stress dependent creep ductility and strain rate model in a ductility exhaustion based damage model,and the equivalent creep strain distributions ahead of crack tips in these specimens were calculated by FEM.Based on crack-tip equivalent creep strain,a unified creep constraint parameter which can characterize both in-plane and out-of-plane constraints was defined.A monotonic correlation line between the CCG rate and Ac can be formed regardless of the in-plane and out-of-plane constraint and choice of sc isolines.This indicates that the parameter Ac may be equally sensitive to both in-plane and out-of-plane constraints,and it is a good unified characterization parameter of in-plane and out-of-plane creep constraint.The results also show that the parameter Ac is load-independent and essentially does not change with creep time(t/tred>0.7),which makes it more convenient for engineering application.(2)Based on extensive three-dimensional finite element analyses,the distributions of the parameter A,along crack fronts(specimen thickness)were calculated,and its capability and applicability for characterizing a wide range of in-plane and out-of-plane creep constraints in different specimen geometries have been comparatively analyzed with the constraint parameters based on crack-tip stress fields(namely R*,h and Tz).The results show that the parameter Ac can simultaneously and effectively characterize a wide range of in-plane and out-of-plane creep constraints,while the parameters R*,h and TZ based on crack-tip stress fields cannot achieve this.The different capabilities of these parameters for characterizing in-plane and out-of-plane creep constraints originate from their underlying theories.(3)Based on the parameter Ac and the experimental creep crack growth rate(CCG)data of different specimen geometries in the literatures,the in-plane and out-of-plane unified constraint-dependent CCG rate equations of Cr-Mo-V steel and 316H steel have been obtained.The predicted CCG rate by using the equation for each specimen agrees well with the experimental data.Based on the two-parameter C*-Ac concept,the equation may be used in CCG life prediction of components with different in-plane and out-of-plane constraints.(4)The constraint parameter Ac and creep crack growth rates of two interface cracks in welded joint C(T)specimens with different in-plane and out-of-plane constraints have been calculated and analyzed.The results show that the CCG rates of the two interface cracks(FGHAZ-BM and FGHAZ-CGHAZ interface cracks)in the welded joint increase with increasing in-plane and out-of-plane constraints.The parameter Ac can characterize both geometry constraint(in-plane and out-of-plane constraints)and material constraint in welded joints.Based on Ac,a unified correlation of geometry and material constraints with creep crack growth rates of welded joints can be established.(5)Unified creep constraint parameter A,for axial and circumferential surface cracks in pressurized pipes have been calculated and investigated by three-dimensional finite element method.It has been shown that the unified creep constraint at the deeper part of crack front is higher than that at the free surface part.The parameter Ac can simultaneously and effectively characterize in-plane and out-of-plane creep constraints in pressurized pipes with different crack sizes.The overall constraint levels of pipe cracks increase with increasing crack depth,length,pipe wall thickness and radius-thickness ratio.The constraint levels of axial cracks are higher than those of circumferential cracks.Based on the FEM results of A,values,the empirical equations of constraint parameter Ac0 at the surface point,constraint parameter Acl at the deepest point and the average constraint parameter Acavg along crack front have been obtained for both axial and circumferential cracks in pressurized pipes.