Essential work of fracture compared to fracture mechanics—towards a thickness independent plane stress toughness

The essential work of fracture (EWF) and the J-integral methods were applied in a study of the effect of the thickness on the cracking resistance of thin plates. The paper discusses two themes: (1) the relationships between the two methods or concepts is elucidated, and (2) a new, thickness independent plane stress toughness parameter is proposed. For that purpose, cracked aluminium 6082O thin plates of 1-6 mm thickness were tested in tension until final separation. The EWF, w_e, and the J-integral at cracking initiation, J_i, increase identically with thickness except at larger thickness for which the increase of J_i levels off. J_i reaches a maximum for 5-6 mm thickness whereas w_e keeps increasing linearly with thickness. This difference is related to the more progressive development of the necking zone in front of the crack tip when thickness increases: at large thickness, cracking initiates well before the neck has developed to its stationary value during propagation. A linear regression on the fracture toughness/thickness curve allows partitioning the two contributions of the work of fracture: the plastic work per unit area for crack tip necking and a plane stress work per unit area for material separation. The pertinence of this new measure of the pure plane stress cracking resistance is critically discussed based on a micromechanical model for ductile fracture. The micromechanical void growth model incorporates void shape effects, which is essential in the low stress triaxiality regime.     

Micromechanical analysis of mechanical heterogeneity effect on the ductile tearing of weldments

The objective of this study is determination of the effect of mechanical heterogeneity on ductile crack initiation and propagation in weldments using micromechanical approach. Welded single-edge notched bend (SENB) specimens were experimentally and numerically analysed. Material properties of welded joint zones were estimated using a combined experimental and numerical procedure; strains on a smooth tensile specimen were determined using ARAMIS stereometric measuring system in order to obtain true stress – true strain curves. High-strength low-alloyed steel was used as base metal, in quenched and tempered condition. J–R curves and crack growth initiation values of fracture mechanics parameter were experimentally and numerically obtained for specimens with a pre-crack in the heat-affected zone (HAZ) and weld metal (WM). The complete Gurson model (CGM) was used in prediction of J–R curves and crack growth initiation. It is shown that the resistance to crack initiation and growth can be predicted using micromechanical analysis, and that the results are significantly affected by mechanical heterogeneity of the weldment.     

Evaluation of critical fracture energy parameter Gfr and assessment of its transferrability

Prediction of maximum load bearing capacity and crack growth for ductile materials using existing models like J-R curve approach has the problem of transferability and the use of micro-mechanical model (e.g. Gurson Tvergaard, and Needleman [Tvergaard V, Needleman A. Analysis of cup cone fracture in a round tensile bar. Acta Metall 1984;32:157-169]) are limited by the requirements of the huge computation time and large numbers of critical metallurgical parameters as input to analysis. Marie and Chapuliot [Marie S, Chapuliot S. Ductile tearing simulation based on local energy criterion. Fatigue Fract Engng Mater Struct 1998;21:215-227] of CEA, France, proposed a simple but convenient ductile crack growth model using critical fracture energy (G_fr) for crack growth and J_i for initiation, both of which are material parameters. They also proposed several schemes, namely, graphical and slope of modified plastic J-integral vs crack growth, J_M-pl − Δa methods for the evaluation of the value of G_fr from specimens as well as from components. In all these methods the role of non-crack displacement in the crack growth process was not considered. The necessary modifications due to non-crack displacement in the above methods to evaluate the values of G_fr was studied and published [Acharyya S, Dhar S, Chattopadhyay J. (2003). The effect of non-crack component on Critical fracture energy on ductile material. Int J Pressure Vessels Piping 2004;81:345-353] by the authors earlier. In this paper, the modified methods and formulation have been applied to evaluate the values of G_fr from experimental and FE simulated results for compact tensile (CT), three point bend (TPB) specimens and also from components like pipes and elbows. Then statistical estimation is done from these G_fr values to assess whether G_fr can be accepted as constant value material parameter. Finally, the mean value of G_fr obtained from statistical computation is used as material constant along with crack initiation toughness parameter (J_i)_SZW to consider crack growth for FE simulation of load vs load-line-displacement (LLD) and load vs crack growth curves for different specimens and components. Finite element simulated results are compared with the experimental results and good matching between the two for several components are found and maximum error in prediction of maximum load is found to be within 12%.     

Measurement of fracture initiation toughness and crack resistance in instrumented Charpy impact testing

A new method has been developed involving direct measurement of the load-line displacement during instrumented Charpy testing. The method uses a laser interferometer to measure displacement in addition to the load-line displacement derived from the load signal. Tests were conducted using fatigue precracked and V-notched test pieces in the temperature range +23°C to −80°C on a conventional ship grade steel, a pressure vessel steel and two welded joints. Good correlation was found between the J_0.2 initiation fracture toughness determined by the multi-specimen method and the J_i fracture toughness determined from single specimens using the new method to detect ductile fracture initiation.     

Estimation and comparative study of JIC using different methods for 20MnMoNi55 steel

Fracture toughness is one of the key input variables to compute critical load of the structural components. The resistance against ductile fracture can be quantified either by the initiation value or by the entire resistance curve. Different standard methods like J_SZW, JSME and ASTM: E1820 etc. are mainly used to estimate the critical crack initiation value from the resistance curve developed by the J-integral test. However, the results vary from method to method and are even inconsistent for the same method. Pehrson and Landes suggested a simple method for estimation of the critical fracture toughness by identifying the critical point corresponding to the maximum load on load–displacement curve. In the present study, different standard methods along with the one suggested by Pehrson and Landes are used to find out the critical fracture toughness using 1T–CT and ½T–CT specimens of the material 20MnMoNi55 steel for varying temperatures and crack size. The results are analyzed to compare the merits of the different methods of estimation of fracture toughness.     

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.     

Influence of notch root radius on ductile rupture fracture toughness evaluation with Charpy-V type specimens

The blunt notch fracture toughness of four types of carbon-manganese steel (ASTM A516 grade 70) has been determined by J-integral tests on Charpy-V type samples with different values of notch root radius, ρ. J-ρ plots, determined using specimens with a notch depth to width ratio, a/w, equal to 0.5, have shown the existence of a limiting ρ value (ρ_eff) below which applied J-intergral values at fracture initiation are constant. These ρ_eff values have been seen to depend only on second-phase particle distribution and not on their volume fraction or on the steel ferritic grain size. The procedure for deriving J-integral values at the onset of stable crack growth from J resistance curves in the case of notches has also been discussed. Experiments with Charpy specimens with a/w = 0.2 do not allow the derivation of meaningful J-ρ plots. In all cases, a ductile fracture criterion based on the constancy of the notch tip strain at rupture initiation has been proved when ρ >ρ_eff.     

The crack growth resistance of thin steel sheets under eccentric tension

The stable crack growth in thin steel sheets is the topic of this paper. The crack opening was observed using a videoextensometry system, allowing the crack extension determination. J_R-curve and δ_R-curve were established from obtained data. The ductile tearing properties of different thin sheets of steel were determined, including the impact of the specimen orientation, from test performed on compact tension specimens loaded under two conditions. The effect of the material, the rolling direction, and loading rate on the crack growth resistance of thin steel sheets was analyzed. In addition to the crack growth resistance, J-integral values for crack initiation were also estimated. The relation between J _i and J_0.2 was assessed using the basic mathematical and statistical methods. This relation was described by a linear regression model.     

Simulation of ductile crack propagation in dual-phase steel

The modified Mohr–Coulomb and the extended Cockcroft–Latham fracture criteria are used in explicit finite-element (FE) simulations of ductile crack propagation in a dual-phase steel sheet. The sheet is discretized using tri-linear solid elements and the element erosion technique is used to model the crack propagation. The numerical results are compared to quasi-static experiments conducted with five types of specimens (uniaxial tension, plane-strain tension, in-plane shear, 45° and 90° modified Arcan) made from a 2 mm thick sheet of the dual-phase steel Docol 600DL. The rate-dependent J ₂ flow theory with isotropic hardening was used in the simulations. The predicted crack paths and the force–displacement curves were quite similar in the simulations with the different fracture criteria. Except for the 45° modified Arcan test, the predicted crack paths were in good agreement with the experimental findings. The effect of using a high-exponent yield function in the prediction of the crack path was also investigated, and it was found that this improved the crack path prediction for the 45° modified Arcan test. In simulations carried out on FE models with a denser spatial discretization, the prediction of localized necking and crack propagation was in better accordance with the experimental observations. In four out of five specimen geometries, a through-thickness shear fracture was observed in the experiments. By introducing strain softening in the material model and applying a dense spatial discretization, the slant fracture mode was captured in the numerical models. This did not give a significant change in the global behaviour as represented by the force–displacement curves.     

Finite element simulation of fracture behaviour for aged duplex stainless steels

In this paper, the local approach model developed by Gurson–Tvergaard has been applied to simulate both the crack initiation and the crack growth of aged duplex stainless steel. The parameters of the Gurson–Tvergaard model have been obtained, from axisymmetric notched specimen testing, as a function of the ageing time at 400°C, the ferrite content of the steel and the stress triaxiality. After that, to simulate the fracture of CT specimens, finite element (FE) calculations have been effected in order to obtain the stress triaxiality value at each point on the process zone ahead of the crack tip of these specimens. The adequate damage parameters concerning triaxiality are determined from the ones obtained at the notched specimens, in order to be used in FE simulations of fracture behaviour. With them, the corresponding J−Δa curves have been simulated as representative of both the crack initiation and crack propagation stages, and compared with experimental results in order to validate the methodology proposed.     

Parametrizing ductile tearing resistance by four parameters

The energy dissipation rate, R, is considered as a measure of resistance to crack extension in elasto-plastic fracture mechanics. It can be re-evaluated from J_R test records of bend and tensile specimens. Three types of R(Δa)-curves are identified. If crack initiation occurs close to or at maximum load, the energy dissipation rate is decreasing with crack extension and approaches a stationary value. This type of R(Δa)-curves can be described by an exponential function with three parameters, namely the initial value, the final stationary value, and a transition length. The cumulative J_R-curves for different specimen geometries can be derived by integration. The three parameters of the R(Δa)-fit together with an integration constant, the initiation value, J_i, characterize ductile fracture resistance both quantitatively and physically interpretable. Constraint effects on R-curves can be quantified in terms of these parameters. A procedure for transferring J_R-curves from one geometry to another is proposed.     

A three-dimensional numerical investigation of fracture initiation by ductile failure mechanisms in a 4340 steel

Fracture initiation in ductile metal plates occurs due to substantial tunneling of the crack in the interior of the specimen followed by final failure of side ligaments by shear lip formation. The tunneled region is characterized by a flat, fibrous fracture surface. This phenomenon is clearly exhibited in a recent experimental investigation [8] performed on pre-notched plates of a ductile heat treatment of 4340 carbon steel. Experimental evidence obtained in [8] suggests that tunneling begins at an average value of J which is significantly lower than the J value at which gross initiation is observed on the free surface. In the present work, fracture initiation in the 4340 steel specimens used in [8] is analyzed by performing a 3-dimensional numerical simulation. A damage accumulation model that accounts for the ductile failure mechanisms of void nucleation, growth, and void coalescence is employed. Results indicate that incipient Cmaterial failure at the center-plane of the 3-dimensional specimen is predicted quite accurately by this computation. Also, good agreement between results obtained at the center-plane of the 3-dimensional specimen and a plane strain analysis, suggests that a local definition of J can be used to characterize fracture initiation in the center-plane of the specimen. Finally, radial and thickness variations of the stress and porosity fields are examined with view of understanding the subsequent propagation of the failure zone.     

A load–deformation formulation with fracture representation based on the J–R curve for tubular joints

This study presents a new fracture formulation to describe the ductile tearing and unstable fracture failure for circular hollow section (CHS) joints under monotonically increasing brace tension. The initiation of the ductile tearing occurs when the crack driving force in an assumed initial shallow crack reaches the material fracture toughness determined from a standard fracture toughness test. The joint behavior prior to the ductile crack initiation follows a previously proposed nonlinear formulation based on the latest strength equations recommended by the International Institute of Welding. The load–deformation characteristics beyond the crack initiation assume that the energy release rate and the amount of crack extension adhere to the experimentally measured J–R curve, prior to the unstable fracture failure. Unstable fracture, which leads to the total loss of the joint capacity, occurs when the crack driving force reaches the maximum fracture resistance determined from the J–R curve test. The proposed load–deformation representation for tubular joints, when implemented in the large-scale K-frame pushover analysis with a material fracture toughness test, predicts successfully the global frame response governed by the joint fracture failure, as observed in the frame test.     

Micromechanical methodology for fatigue in cardiovascular stents

A finite element based micromechanical methodology for cyclic plasticity and fatigue crack initiation in cardiovascular stents is presented. The methodology is based on the combined use of a (global) three-dimensional continuum stent-artery model, a local micromechanical stent model, the development of a combined kinematic–isotropic hardening crystal plasticity constitutive formulation, and the application of microstructure sensitive crack initiation parameters. The methodology is applied to 316L stainless steel stents with random polycrystalline microstructures, based on scanning electron microscopy images of the grain morphology, under realistic elastic–plastic loading histories, including crimp, deployment and in vivo systolic–diastolic cyclic pressurisation. Identification of the micromechanical cyclic plasticity and failure constants is achieved via application of an objective function and a unit cell representative volume element for 316L stainless steel. Cyclic stent deformations are compared with the J₂-predicted response and conventional fatigue life prediction techniques. It is shown that micromechanical fatigue analysis of stents is necessary due to the significant predicted effects of material inhomogeneity on micro-plasticity and micro-crack initiation.     

Essential work of fracture analysis of the tearing of a ductile polymer film

The fracture behaviour of a 0.5 mm thick ethylene-propylene block copolymer, previously evaluated using the essential work of fracture method, has been analyzed again in more detail, using different plots, allowing the determination of the crack initiation displacement and stress. In such plots is evidenced that the specific essential work of fracture, w_e, corresponds to the energy just up to crack initiation value that can be related with J₀. Also, it has been found a novel relationship between the plastic term, βw_p and the crack initiation stress, σ_i.     

A model for the static fracture toughness of ductile structural steel

Fracture of ductile structural steels generally occurs after void initiation, void growth and void coalescence. In order for ductile fracture of structural steels to occur, energy must be spent to induce void initiation and void growth. Therefore, fracture toughness for ductile fracture should be contributed from void initiation and void growth. On the basis of this suggestion static fracture toughness (K_IC) of ductile structural steels is decomposed into two parts: void nucleation-induced fracture toughness (denoted as K_IC.n) and void growth-induced fracture toughness (K_IC.g). K_IC.n, defined as the stress intensity factor at which voids ahead of a crack begins to form, is calculated from crack tip strain distribution and void nucleation strain distribution. In contrast, K_IC.g is determined by the void growth from the beginning of void nucleation to void coalescence. Therefore, K_IC.g relates to the void sizes and void distribution. In this paper, the expression for K_IC.g is given from the void sizes directly from fracture surfaces. The relationship between K_IC.n, K_IC.g and K_IC is expressed in the form (K_IC)²=(K_IC.n)²+(K_IC.g)². The newly developed model was applied to the fracture toughness evaluation of three structural steels (SN490, X65 and SA440), and the theoretical calculation agrees with the experimental results.     

A model for the static fracture toughness of ductile structural steel

Fracture of ductile structural steels generally occurs after void initiation, void growth and void coalescence. In order for ductile fracture of structural steels to occur, energy must be spent to induce void initiation and void growth. Therefore, fracture toughness for ductile fracture should be contributed from void initiation and void growth. On the basis of this suggestion static fracture toughness (K_IC) of ductile structural steels is decomposed into two parts: void nucleation-induced fracture toughness (denoted as K_IC.n) and void growth-induced fracture toughness (K_IC.g). K_IC.n, defined as the stress intensity factor at which voids ahead of a crack begins to form, is calculated from crack tip strain distribution and void nucleation strain distribution. In contrast, K_IC.g is determined by the void growth from the beginning of void nucleation to void coalescence. Therefore, K_IC.g relates to the void sizes and void distribution. In this paper, the expression for K_IC.g is given from the void sizes directly from fracture surfaces. The relationship between K_IC.n, K_IC.g and K_IC is expressed in the form (K_IC)²=(K_IC.n)²+(K_IC.g)². The newly developed model was applied to the fracture toughness evaluation of three structural steels (SN490, X65 and SA440), and the theoretical calculation agrees with the experimental results.     

J–R curves corrected by load-independent constraint parameter in ductile crack growth

The constraint effect on J–resistance curves of ductile crack growth is considered under the condition of two-parameter J–Q^* controlled crack growth, where Q^* is a modified parameter of Q in the J–Q theory. Both J and Q^* are used to characterize the J–R curves with J as the loading level and Q^* as a constraint parameter. It is shown that Q^* is independent of applied loading under large-scale yielding or fully plastic deformation, and so Q^* is a proper constraint parameter during crack growth. An approach to correct constraint effects on the J–R curve is developed, and a procedure of transferring the J–R curves determined from standard ASTM procedure to nonstandard specimens or real cracked structures is outlined.The test data of fracture toughness, J_IC, and tearing modulus, T_R, by Joyce and Link (Engng. Fract. Mech. 57(4) (1997) 431) for a single-edge notched bend specimen with various depth cracks are employed to demonstrate the efficiency of the present approach. The variation of J_IC and T_R with the constraint parameter Q^* is obtained, and then a constraint-corrected J–R curve is constructed for the test material of HY80 steel. Comparisons show that the predicted J–R curves can match well with the experimental data for both deep and shallow cracked specimens over a reasonably large amount of crack extension.Finally, the present approach is applied to predict the J–R curves of ductile crack growth for five conventional fracture specimens. The results show that the effect of specimen geometry on the J–R curves is generally much larger than the effect of specimen sizes, and larger specimens tend to have lower crack growth resistance curves.     

Some contribution to process zone fracture mechanics

The mechanism of the ductile fracture is studied theoretically for the Al Alloy 7075-T6 specimens. A model for the interaction of a crack tip with a void nearby is analyzed by using the Modified Gurson's Model. Taking fracture criterion into consideration, the analysis of a crack propagation is carried out and besides the distribution of the equivalent plastic strain, the void volume fraction f and the localization are obtained. Microcracks nucleate on the ligament between crack and void, and grow and coalesce each other, and at last the main crack thus formed coalesces with the void and the coalescence of the crack and void is completed. And these phenomenon occurs in the localized region.The initiation of the microcrack of 7075 occurs at small J and the microcrack penetration between crack and void occurs at larger J, and the propagation does not occur smoothly. These results coincide with the results of the experiments by FRASTA (FRActure Surface Topographic Analysis) and Fractography.     

Ductile fracture of edge-cracked beam under dynamic electromagnetic bending force

Dynamic and ductile fracture of edge-cracked beam made of Type 304 stainless steel under electromagnetic bending force is studied experimentally as well as theoretically. In the theoretical part, we calculate the extended J-integral with the effect of both electromagnetic force and thermal stress caused by the Joule heating concerning the fracture phenomena due to the electromagnetic force. In the experiments, the edge-cracked beam specimens of Type 304 stainless steel are fractured under the electromagnetic force, measuring the crack initiation time, the crack velocity etc. Finally, the theoretical and the experimental results are compared.