Two-parameter characterization of elastic-plastic crack front fields: Surface cracked plates under tensile loading

In this paper the J-Q two-parameter characterization of elastic-plastic crack front fields is examined for surface cracked plates under uniaxial and biaxial tensile loadings. Extensive three-dimensional elastic-plastic finite element analyses were performed for semi-elliptical surface cracks in a finite thickness plate, under remote uniaxial and biaxial tension loading conditions. Surface cracks with aspect ratios a/c = 0.2, 1.0 and relative depths a/t = 0.2, 0.6 were investigated. The loading levels cover from small-scale to large-scale yielding. In topological planes perpendicular to the crack fronts, the crack stress fields were obtained. In order to facilitate the determination of Q-factors, modified boundary layer analyses were also conducted. The J-Q two-parameter approach was then used in characterizing the elastic-plastic crack front stress fields along these 3D crack fronts. Complete distributions of the J-integral and Q-factors for a wide range of loading conditions were obtained. It is found that the J-Q characterization provides good estimate for the constraint loss for crack front stress fields. It is also shown that for medium load levels, reasonable agreements are achieved between the T-stress based Q-factors and the Q-factors obtained from finite element analysis. These results are suitable for elastic-plastic fracture mechanics analysis of surface cracked plates.     

Approximate elastic-plastic J estimates of cylinders with off-centred circumferential through-wall cracks

This paper provides approximate J estimates for off-centred, circumferential through-wall cracks in cylinders under bending and under combined tension and bending. The proposed method is based on the reference stress approach, where the dependence of elastic and plastic influence functions of J on the cylinder/crack geometry, the off-centred angle and strain hardening is minimised through the use of a proper normalising load. Based on published limited FE results for off-centred, circumferential through-wall cracks under bending, such normalising load is found, based on which the reference stress based J estimates are proposed for more general cases, such as for a different cylinder geometry and for combined loading. Comparison of the estimated J with extensive FE J results shows overall good agreements for different crack/cylinder geometries and for combined tension and bending, which provides sufficient confidence in the use of the proposed method for fracture mechanics analyses of off-centred circumferential cracks. Furthermore, the proposed method is simple to use, giving significant merits in practice.     

Correlation of fracture behavior in high pressure pipelines with axial flaws using constraint designed test specimens. Part II: 3-D effects on constraint

This study describes an extensive set of 3-D analyses conducted on conventional fracture specimens, including pin-loaded and clamped SE(T) specimens, and axially cracked pipes with varying crack configurations. The primary objective is to examine 3-D effects on the correlation of fracture behavior for the analyzed crack configurations using the J-Q methodology. An average measure of constraint over the crack front, as given by an average hydrostatic parameter, denoted Q_avg, is employed to replace the plane-strain measure of constraint, Q. Alternatively, a local measure of constraint evaluated at the mid-thickness region of the specimen, denoted Q_Z0, is also utilized. The analysis matrix considers 3-D numerical solutions for models of SE(T) fracture specimens with varying geometries (i.e., different crack depth to specimen width ratio, a/W, as well as different loading point distance, H) and test conditions (pin-loaded ends vs. clamped ends). The 3-D numerical models for the cracked pipes cover different crack depth to pipe wall thickness ratio, a/t, and a fixed crack depth to crack length ratio, a/c. The extensive 3-D numerical analyses presented here provide a representative set of solutions which provide further support for using constraint-designed SE(T) specimens in fracture assessments of pressurized pipes and cylindrical vessels.     

A study to estimate crack length using the separability parameter Spb in steels

The separability property with S_pb parameter was used in this work to estimate the instantaneous crack length in pre-cracked specimens. A test matrix, pre-cracked ASTM C(T), SE(B) specimens and non-standard A(B) arc-shaped geometry was prepared. Materials were ASTM 387-Gr.22 2.25Cr-1.0Mo steel, an API Gr.N80 and HSLA welded joints. Initial and final crack lengths were measured on the crack surface and instantaneous crack length was determined by the compliance method to compare against the values of crack length estimated using the S_pb parameter. The difference between the resulting values was less than 15%Δa suggested as reference in ASTM E1820-96.     

Elastic T-stress for cracks in test specimens subjected to non-uniform stress distributions

Finite element analyses have been conducted to calculate elastic T-stress solutions for cracked test specimens. The T-stress solutions are presented for single edge cracked plates, double edge crack plates and centre cracked plates. Uniform, linear, parabolic or cubic stress distributions were applied to the crack face. The results for uniform and linear stress distributions were used to derive weight functions for T-stress for the corresponding specimens. The weight functions for T-stress are then verified against several linear and non-linear stress distributions. The derived weight functions are suitable for the T-stress calculation for cracked specimens under any given stress field.     

Accounting for porosity, time and temperature dependency in fracture mechanics concepts on polyvinylidene fluoride material

The polyvinylidene fluoride (PVDF) under study is a semi-crystalline polymer that exhibits sensitivity of mechanical properties to both strain rate and temperature. Furthermore, this material is subjected to a significant cavitation during deformation. A comprehensive experimental database was built in order to analyze the fracture behaviour in the ductile to brittle transition domain. Tensile tests were carried out on smooth and notched specimens at temperatures ranging from −50 °C to 20 °C. The results were used to determine temperature-dependent material parameters by using the mechanics of porous media. The obtained set of parameters was validated on two kinds of pre-cracked specimens, by using the local approach of fracture mechanics. With the help of a finite element code, both global and local approaches of fracture mechanics were shown to complement one another: whereas classical formulae of J-integral fail to characterize crack initiation for this PVDF, the present methodology allowed the plot of J_1C values with respect to temperature.     

Elastic-plastic fracture mechanics assessment of test data for circumferential cracked pipes

This paper presents experimental validation of two reference stress based methods for circumferential cracked pipes. One is the R6 method where the reference stress is defined by the plastic limit load. The other is the enhanced reference stress method, recently proposed by the authors, where the reference stress is defined by the optimised reference load. Using 38 published pipe test data, the predicted maximum instability loads according to both methods are compared with the experimental ones for pipes with circumferential through-thickness cracks and with part circumferential surface cracks. It is found that the R6 method gives conservative estimates of the maximum loads for all cases. Ratios of the experimental maximum load to the predicted load range from 0.54 to 0.98. On the other hand, the proposed method gives overall closer maximum loads than R6, compared to the experimental data. However, for part through-thickness surface cracks, the estimated loads were slightly non-conservative for four cases, and possible reasons are fully discussed.     

Study on the behavior of elastic-plastic fracture under mixed I+II mode loading in aluminum alloy Ly12-J-integral analysis

The elastic-plastic fracture behavior of aluminum alloy Ly12 under mixed I+II mode loading was studied by finite element method and fracture test. A mixed mode elastic-plastic fracture criterion of J-integral was proposed by using the J-resistance curve, and the maximum fracture effective plastic strain _p max of different mixed ratios at crack tip were also calculated. The results show that(1) the initiation J-integral values of different mixed ratios have the equation

Elastic-plastic fracture mechanics analyses of circumferential through-wall cracks between elbows and pipes

The present work proposes a method for elastic-plastic fracture mechanics analysis of the circumferential through-wall crack in weldment joining elbows and attached straight pipes, subject to in-plane bending. Heterogeneous nature of weldment is not explicitly considered and thus, the proposed method assumes cracks in homogeneous materials. Based on small strain finite element limit analyses using elastic-perfectly plastic materials, closed-form limit loads for circumferential through-wall cracks between elbows and straight pipes under bending are given. Then applicability of the reference stress-based method to approximately estimate J and crack opening displacement (COD) is evaluated. It was found that the limit moments for circumferential cracks between elbows and attached straight pipes can be much lower than those for cracks in straight pipes, particularly for a crack length of less than 30% of the circumference; this result is of great interest in practical cases. This result implies that, if one assumes that the crack locates in the straight pipe, limit moments could be overestimated significantly, and accordingly, reference stress-based J and COD could be significantly overestimated. For the leak-before-break analysis, accurate J and COD estimation equations based on the reference stress approach are proposed.     

Effect of crack depth on the shift of the ductile-brittle transition curve of steels

Nuclear reactor pressure vessel (RPV) steels degrade due to neutron irradiation during normal operation. As a result, the ductile-brittle transition curve of the steel shifts to higher temperature which decreases operation margins in both the temperature and pressure. The loss of these margins however can be offset somewhat by appealing to arguments based on constraint of potential/postulated shallow cracks. In this paper, it is demonstrated that the fracture toughness values for shallow flaws are higher than those determined from standard deep cracked test specimens based on constraint consideration. The J-A₂ three-term solution is used to characterize the crack-tip stress field where J represents the level of loading and A₂ quantifies the level of constraint. Based on the RKR cleavage model, procedures to quantify the temperature shift between specimens with different constraint levels are developed. The experimental data by Sherry et al. [Sherry AH, Lidbury DPG, Beardsmore DW. Validation of constraint based structural integrity assessment methods. Final report, Report No. AEAT/RJCB/RD01329400/R003, AEA Technology, UK, 2001] for the A533B RPV steel are used to demonstrate the procedure and it is shown that the ductile-brittle transition curve shifts to lower temperature from high constraint to low constraint specimens.     

Application of fracture mechanics for weld integrity assessment

The structural integrity assessment of a weld joint by conventional techniques is inadequate, because of unavoidable defects in the weld composite. The stress situation in a component having a defect is quite different from that of a homogeneous material. The significance of fracture mechanics to deal with such integrity assessments is brought out. A brief review on the basic formulations in the application of fracture mechanics is followed by established guidelines for evaluating the integrity of engineering components containing crack-like defects.     

Residual stresses and fracture mechanics analysis of a crack in welds of high strength steels

This study presented the characteristics of residual stresses in welds of high strength steels (POSTEN60, POSTEN80) whose tensile strengths were 600 MPa and 800 MPa, respectively. Three-dimensional thermal elastic-plastic analyses were conducted to investigate the characteristics of welding residual stresses in welds of high strength steels through the thermal and mechanical properties at high temperatures obtained from the elevated temperature tensile tests. A finite element analysis method which can calculate the J-integral for a crack in a residual stress field was developed to evaluate the J-integral for a centre crack when mechanical stresses were applied in conjunction with residual stresses.The results show that the volumetric changes associated with the austenite to martensite phase transformation during rapid cooling after welding of high strength steels significantly influence on the development of residual stresses in the weld fusion zone and heat-affected zone. For a centre crack in welds of high strength steels where only residual stresses are present, increased tensile strength of the steel, increased the J-integral values. The values of the J-integral for the case when mechanical stresses are applied in conjunction with residual stresses are larger than those for the case when only residual stresses are present.     

Continuum Shape Sensitivity analysis of a mode-I fracture in functionally graded materials

This paper presents a new method for conducting a continuum shape sensitivity analysis of a crack in an isotropic, linear-elastic, functionally graded material. This method involves the material derivative concept from continuum mechanics, domain integral representation of the J-integral and direct differentiation. Unlike virtual crack extension techniques, no mesh perturbation is needed to calculate the sensitivity of stress-intensity factors. Since the governing variational equation is differentiated prior to the process of discretization, the resulting sensitivity equations are independent of approximate numerical techniques, such as the meshless method, finite element method, boundary element method, or others. In addition, since the J-integral is represented by domain integration, only the first-order sensitivity of the displacement field is needed. Several numerical examples are presented to calculate the first-order derivative of the J-integral, using the proposed method. Numerical results obtained using the proposed method are compared with the reference solutions obtained from finite-difference methods for the structural and crack geometries considered in this study.     

Experimental T33-stress formulation of test specimen thickness effect on fracture toughness in the transition temperature region

This paper describes a study of the test specimen thickness effect on fracture toughness of a material, in the transition temperature region, for CT specimens. In addition we studied the specimen thickness effect on the T₃₃-stress (the out-of-plane non-singular term in the series of elastic crack-tip stress fields), expecting that T₃₃-stress affected the crack-tip triaxiality and thus constraint in the out-of-plane direction. Finally, an experimental expression for the thickness effect on the fracture toughness using T₃₃-stress is proposed for 0.55% carbon steel S55C. In addition to the fact that T₃₃ (which was negative) seemed to show an upper bound for large B/W, these results indicate the possibility of improving the existing methods for correlating fracture toughness obtained by test specimen with the toughness of actual cracks found in the structure, using T₃₃-stress.     

Debonding analysis of fiber-reinforced-polymer strengthened beams: Cohesive zone modeling versus a linear elastic fracture mechanics approach

A linear elastic fracture mechanics (LEFM) approach and a cohesive interface (cohesive zone) modeling approach to the debonding analysis of concrete beams strengthened with externally bonded fiber-reinforced-polymer (FRP) strips are studied and compared. The analytical models that are based on the two approaches are presented and discussed. The cohesive interface model is formulated using a potential function and it takes into account the shear effects, the effect of the peeling stresses, and the coupling of the shear and the peeling effects. This model takes the form of a set on nonlinear differential equations. The LEFM model combines stress analysis using the high order theory and fracture analysis using the concepts of the energy release rate and the J-integral. In addition, an algorithm that converts the results of the LEFM model into the equilibrium path of the debonding process is developed. The main advantages and disadvantages of the two approaches are also discussed. The two approaches are compared in terms of their applicability to quantify and describe the debonding process in various cases that include a single shear test, an edge peeling test, and a beam specimen strengthened with FRP.     

On the application of the damage work density as a new initiation criterion for ductile fracture

In this paper the ‘damage work’ proposed by Chaouadi et al. is used to formulate an energy crack initiation criterion to describe ductile crack initiation. The traditional assessment of structural integrity by the J-integral, a property of elastic-plastic fracture mechanics is compared. Two free-cutting and one structural steel are investigated. The measured values for the critical damage work density at initiation W_di are compared with values for copper and RPV steel. As the fracture mechanical approach is limited to sharp cracks in the material (high-constraint stress state) the present damage mechanics approach is regarded as important as a more general concept closer to reality. While old void growth models of damage mechanics cannot formulate a simple criterion for crack initiation the applied damage work reaches a constant value at initiation W_di which is independent of the stress state during the deformation process. We recommend W_di as a material property of toughness for testing and engineering purposes.     

Fractal modeling of the J-R curve and the influence of the rugged crack growth on the stable elastic-plastic fracture mechanics

In this paper, fractal geometry is used to modify the Griffith-Irwin-Orowan classical energy balance. Crack fractal geometry is introduced in the elastic-plastic fracture mechanics by means of the Eshelby-Rice J-integral and the influence of the ruggedness of the crack surface on the quasistatic crack growth is evaluated. It is shown that the rising of the J-R curve correlates to the topological ruggedness dimension of the crack surface. Results from fracture experiments are shown to be very well fitted with the proposed model, which is shown to be a unifying approach for fractal models currently used in fracture mechanics.     

On the use of constraint parameter A2 determined from displacement in predicting fracture event

The constraint based fracture mechanics methodology, J–A₂ method, has been used to interpret cleavage fracture recently. In all previous studies, the constraint parameter A₂ was determined by stresses analytically calculated from finite element analyses (FEA). In the current paper, it is first demonstrated that A₂ can be measured during a fracture test using the crack tip opening displacement (CTOD). A single-edge-notched specimen under bending (SENB) is used to compare the A₂ values determined from δ₅ displacement and the stress components. Finally, cleavage fracture toughness values for A533-B reactor pressure vessel (RPV) steel at −40°C obtained from test programs at Oak Ridge National Laboratory (ORNL) and the University of Kansas (KU) are interpreted using the J–A₂ analytical model. Particular emphasis is placed on using the A₂ determined from CTOD to characterize the fracture event. It is demonstrated that the effects of crack depth (shallow vs deep) and specimen size (small vs large) on the fracture toughness from the test programs can be interpreted and predicted using J and the constraint level A₂ measured from the displacement.     

The effect of specimen thickness on the experimental and finite element characterization of CTOD in extra deep drawn steel sheets

Recent experimental results by us have indicated that the load-drop technique can serve as a valid fracture criterion for predicting elastic-plastic fracture in extra deep drawn (EDD) steel sheets or in predominantly plane stress conditions. The purpose of this investigation is to examine the validity of aJ-integral as a fracture parameter and theJ-CTOD relation for the determination of critical CTOD in predominantly plane stress fracture (CTOD-crack tip opening displacement). Fracture tests were performed and experimental results were generated on fracture behaviour of EDD (0·06%C) steel sheets with CT specimens and using ‘load-drop’ as a fracture criterion. Critical CTOD was determined by using theJ-CTOD relation in addition to several existing techniques. A full 3-D finite element model was formulated to verify the critical load, critical CTOD and plastic-zone size. The critical CTOD was shown to increase with increasing specimen thickness and appeared to be approaching a higher limiting value. The characteristic features of predominantly plane stress fracture or general yielding fracture mechanics are summarized in conclusion