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Effect of Residual Stress on Cleavage Fracture Toughness by Using Cohesive Zone Model

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Effect of Residual Stress on Cleavage Fracture Toughness by Using Cohesive Zone Model Fatigue & Fracture of Engineering Materials & Structures doi: 10.1111/j.1460-2695.2011.01550.x Effect of residual stress on cleavage fracture toughness by using cohesive zone model X. B. REN1,Z.L.ZHANG1 andB.NYHUS2 1Department of Structural Engineering, Norwegian University of Science and Technology (NTNU), N-7491, Trondheim, Norway, 2SINTEF Materials and Chemistry, N-7465 Trondheim, Norway Received in final form 13 Dec 2010 ABSTRACT This study presents the effect of residual stresses on cleavage fracture toughness by using the cohesive zone model under mode I, plane stain conditions. Modified boundary layer simulations were performed with the remote boundary conditions governed by the elastic K-field and T-stress. The eigenstrain method was used to introduce residual stresses into the finite element model. A layer of cohesive elements was deployed ahead of the crack tip to simulate the fracture process zone. A bilinear traction–separation-law was used to characterize the behaviour of the cohesive elements. It was assumed that the initiation of the crack occurs when the opening stress drops to zero at the first integration point of the first cohesive element ahead of the crack tip. Results show that tensile residual stresses can decrease the cleavage fracture toughness significantly. The effect of the weld zone size on cleavage fracture toughness was also investigated, and it has been found that the initiation toughness is the linear function of the size of the geometrically similar weld. Results also show that the effect of the residual stress is stronger for negative T-stress while its effect is relatively smaller for positive T-stress. The influence of damage parameters and material hardening was also studied. Keywords cleavage toughness; cohesive zone model; eigenstrain method; modified boundary layer model; residual stress. INTRODUCTION its highly localized character of the failure mechanism.5 Understanding how residual stresses influence the cleav- Residual stresses associated with welding are unavoidable age fracture behaviour becomes more and more impor- and play an important role in structural integrity of engi- tant when high-strength steels are increasingly utilized in neering components. It has been shown that the residual offshore industry. stresses influence both the crack driving force1 and crack- Experimental work undertaken by Mirzaee-Sisan et al.7 tip constraint.2–4 Crack-tip constraint arises from differ- indicated an apparent reduction in mean cleavage fracture ences in the level of opening stress near the crack tip and toughness of an A553-B ferritic steel of 50% from con- affects the transferability of material toughness, which is ventional fracture toughness data due to residual stresses. a key issue in application of fracture mechanics to assess Panontin and Hill6 utilized the Ritchie–Knott–Rice the integrity of structural components.5 Cleavage fracture (RKR)8 model to predict the effect of residual stresses featured with negligible plastic tearing before final failure on brittle fracture initiation and found that the constraint is often the most dangerous failure mode. It occurs by the generated by the residual stress decreases the initiation unstable propagation of microcracks formed within grain toughness of brittle fracture. boundary particles by twinning or slip dislocation pile-ups Micromechanical models using continuum representa- and then grows into the ferrite matrix under the action of tion of stress and strain are generally used to predict lo- tensile stress.6 The cleavage fracture toughness exhibits cal conditions for cleavage fracture. For cleavage fracture sensitivity to the local stress and deformation fields due to to happen, the opening stress should reach the critical σ value c at a certain distance from the crack tip rc or 9 Correspondence: Z. L. Zhang. E-mail: [email protected] within a certain volume in front of the crack tip. This 592 c 2011 Blackwell Publishing Ltd. Fatigue Fract Engng Mater Struct 34, 592–603 RESBrittle 593 physical scale must be considered in studying the mi- cromechanisms of fracture in order to consider mi- crostructural features necessary for the physical failure mechanism. It was assumed in the RKR model that occur- rence of cleavage fracture requires that the opening stress σ σ ∗ 22 at the crack tip exceeds the fracture stress f over a ∗ critical distance lb which is on the order of the grain size of the steel. Previous studies concerning cleavage fracture indicate that the critical fracture stress ranges from three to four times the yield strength of the material, and that Fig. 1 Schematic plot of the assumption made in this study. is relatively independent of temperature and strain rate. Estimates of the characteristic length or distance in mild steels range from 2 to 5 grain diameters.6 However, in real elastic–plastic materials, large plastic deformations are of- introduced. The cohesive zone model was used to model ten necessary to initiate the cleavage fracture. Therefore, the fracture process zone (FPZ). The material property Neimitz et al.9 proposed an alternative formulation of the mismatch between the weld metal and base metal has not RKR criterion. The cleavage fracture was demonstrated been taken into account. as a synergistic action of the stress and deformation at the critical moment. It has been demonstrated that for fracture to occur it is not sufficient that the opening stress Finite element model reaches the critical value alone, but it is also necessary that The MBL model used for this study consists of a weld the location of this maximum from the crack tip must be region located in the centre of the model and an outer ≥ over the distance l lc,wherelc is considered as a material base metal region, and a sharp crack was embedded in the parameter. centre of weld. The load was applied to the remote edges The current study investigated the effect of the residual of the model through a displacement field (u, v) governed stresses on the cleavage fracture toughness by employing by the elastic asymptotic stress field of a plane strain mode a modified boundary layer (MBL) model under mode I I crack: plane strain conditions with the remote boundary gov- + v erned by elastic K-field and T-stress. The cohesive zone ,θ = 1 r 1θ − v − θ u(r ) K I cos (3 4 cos ) model was utilized to simulate the cleavage fracture, and E 2π 2 the failure was assumed to occur when the opening stress 1 − v2 +T r cos θ at the first integration point of the first cohesive element E (1) ahead of the crack tip drops to zero, as illustrated in Fig. 1. 1 + v r 1 v(r,θ) = K sin θ (3 − 4v − cos θ) The assumption is based on the modified RKR criterion I E 2π 2 proposed by Neimitz et al.,9 and the large strain effect was v(1 + v) −T r sin θ, also considered in the analyses. Based on this assumption, E the effect of the residual stresses on cleavage toughness = / − v2 was investigated by comparing the case including residual where K I EJ 1 under plane strain condition, stress effect with the reference case. E is Young’s modulus, ν is Poisson’s ratio, and r and θ are polar coordinates centred at the crack tip with θ = 0 corresponding to the crack tip. NUMERICAL PROCEDURE The finite element computations were performed using ABAQUS.10 The radius of the MBL model was taken as Problem description 200 mm. A layer of uniform-sized cohesive elements was This study concerns an ideal problem. A large round deployed along the central line ahead of the crack tip to cylinder with a weld in the centre was studied. The cylin- simulate the fracture process. The length of the cohesive der was simulated by a 2D plane strain MBL model with element-layer is 20 mm, and the size of the uniform co- the remote boundary governed by the elastic K-field and hesive element lc is 0.1 mm. The thickness of the cohesive − T-stress. The analysis procedure consists of the following elements is 2.5 × 10 4 mm. The weld metal and base metal steps: (1) enforce a welding procedure, which introduce region of the model was meshed by standard full integra- a residual stress field; (2) introduce a sharp crack; (3) ap- tion four-node 2D plane strain elements. The cohesive ply the external load, as illustrated in Fig. 2. It should elements are standard cohesive element COH2D4. The be noted that the contact between the upper and lower finite element model has 4992 elements and the meshes free surfaces were considered when the residual stress was areshowninFig.3. c 2011 Blackwell Publishing Ltd. Fatigue Fract Engng Mater Struct 34, 592–603 594 X. B. REN et al. Fig. 2 Illustration of the problem, (a) the round cylinder; (b) welding at the centre and a sharp crack is introduced and (c) the external load applied. 207,000 MPa, yield stress σ0 is 460 MPa, which corre- sponds to a typical modern pipeline steel. ε0 = σ0/E is the yield strain. n is the plastic strain hardening exponent, and low n represents low hardening. Different thermal expansion coefficients of the base metal and weld metal are assumed to introduce the residual stresses into the model by so-called eigenstrain method. It should be noted that the thermal expansion coefficients here are not physical thermal coefficients, but are used to introduce the residual stress into the computational model. The eigenstrain method was also called ‘inherent strain’ method when first introduced by Ueda et al.11 The concept of the eigenstrain method is that the source of residual stress is an incompatible strain field caused by plastic deformation, thermal strains and phase-transformation, etc.12 Thus, if the distribution of the eigenstrain is known, the distribution of residual stresses can be obtained through linear elastic calcula- tion by using the finite element method.
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