A model for the dynamic fracture toughness of ductile structural steel

We assume in this paper that the dynamic fracture toughness K_Id of ductile structural steels is dependent on void nucleation and void growth. The void nucleation-induced dynamic fracture toughness K_Id·n and the void growth-induced dynamic fracture toughness K_Id·g were obtained by modifying the void nucleation-induced and void growth-induced static fracture toughness models, respectively, considering the effect of strain rate and local temperature. By the relationship between the void nucleation-induced dynamic fracture toughness K_Id·n and the void growth-induced dynamic fracture toughness K_Id·g((K_Id)²=(K_Id·n)²+(K_Id·g)²) dynamic fracture toughness K_Id could be quantitatively evaluated. With this model the dynamic fracture toughness of two structural steels (X65 and SA440) was assessed, and the causes for the differences between the static and dynamic fracture toughness were also discussed.     

Effect of pre-strain on fracture toughness of ductile structural steels under static and dynamic loading

The ductile fracture process consists of void nucleation, growth and coalescence. The whole ductile process can be divided into two successive steps: (I) the initial state to void nucleation, followed by (II) void growth up to void coalescence. Based on this suggestion, resistance to ductile fracture could be divided into the resistance to stage I and stage II, and accordingly the whole fracture toughness could be regarded to be due to contributions from stages I and II. The fracture toughness contributed from the two steps is, respectively, denoted as void nucleation-contributed fracture toughness and void growth-contributed fracture toughness. The effect of plastic pre-strain on the fracture toughness of ductile structural steels under static and dynamic loading (4.9 m/s) within the ductile fracture range was evaluated by summing contributions due to void nucleation-contributed and void growth-contributed fracture toughness. The effect of strain rate on fracture toughness was also investigated by the same means. The results show that both plastic pre-strain and high-speed loading decrease the void nucleation-contributed fracture toughness while their effects on the void growth-contributed fracture toughness depend on the variations in strength and ductility. Moreover, fracture toughness of structural steels generally decreases with increasing strain rate.     

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.     

Experimental and numerical investigation of thickness effect on ductile fracture toughness of steel alloy sheets

Effect of thickness on ductile fracture toughness of plates made of steel alloy GOST 08Ch22N6T is investigated experimentally. Multiple specimen tests for determining fracture toughness have been conducted using compact tension (CT) specimens with thicknesses of 1.25, 1.64 and 4.06 mm according to standard test method ASTM E813. The results show the significant effect of thickness on fracture toughness. It is observed that in low thickness, J_c increases with the thickness increase until it reaches a maximum; however, further increase in the thickness causes the J_c-value to decrease. Two-dimensional finite element analysis is also performed to reproduce the experimental results. The comparison shows a very good agreement.     

A model for the dynamic fracture toughness of ductile structural steel

We assume in this paper that the dynamic fracture toughness K_Id of ductile structural steels is dependent on void nucleation and void growth. The void nucleation-induced dynamic fracture toughness K_Id·n and the void growth-induced dynamic fracture toughness K_Id·g were obtained by modifying the void nucleation-induced and void growth-induced static fracture toughness models, respectively, considering the effect of strain rate and local temperature. By the relationship between the void nucleation-induced dynamic fracture toughness K_Id·n and the void growth-induced dynamic fracture toughness K_Id·g((K_Id)²=(K_Id·n)²+(K_Id·g)²) dynamic fracture toughness K_Id could be quantitatively evaluated. With this model the dynamic fracture toughness of two structural steels (X65 and SA440) was assessed, and the causes for the differences between the static and dynamic fracture toughness were also discussed.     

Anisotropic ductile fracture of Al 2024 alloys

The anisotropic fracture of the 2024-T351 aluminium alloy is investigated using a micromechanics-based damage model accounting for the effect of the void aspect ratio and void distribution. The 2024-T351 Al alloy contains precipitation free bands in which most void nucleating particles are located. The presence of these bands, which are parallel to the rolling direction, primarily controls the distribution of damage and overall fracture anisotropy. The primary void nucleating particles also present a preferential elongation in the rolling direction. These key microstructural features have been determined using quantitative characterisation methods. The effects of void shape and void spacing on the fracture behaviour are elucidated by means of FE cell calculations. FE simulations of cylindrical notched round bars loaded in different orientations are made and compared with experimental data, allowing a better understanding of the damage process as well as the limitations of the modelling approach.     

Precracking high speed steel for fracture toughness testing

Fracture toughness testing of high speed steel, which has a high fatigue strength and low fracture toughness, is a problem because fatigue cracks are difficult, or impossible, to initiate at a maximum fatigue stress intensity of $\text{0.7 K}{}_{\mathrm{<mtext>IC</mtext>}}$, as specified. A method of initiation by the use of an electric pen and subsequent fast propagation by fatigue has been studied and a procedure developed to give accurate, reproducible values of $\text{K}{}_{\mathrm{<mtext>IC</mtext>}}$ on subsequent fracture toughness testing.     

Large scale testing and statistical analysis of dynamic fracture toughness of ductile cast iron

The present paper deals with the experimental determination and statistical analysis of dynamic fracture toughness values of ductile cast iron. K_Id data from 140 mm thick single edge bend specimens of two dynamic fracture toughness test series on ductile cast iron from heavy-walled castings were analysed.At first, the statistical analysis of data at −40 °C was done based on ASME Code Case N-670 using a two-parameter Weibull distribution function. Weibull analyses of three samples covering different pearlite contents (?4%, ?9%, ?20%) were performed and characteristics of the distribution functions as well as two-sided confidence intervals were calculated. The calculated characteristics show that K_Id of ductile cast iron decreases with increasing pearlite content.In a second step, the applicability of the Master curve procedure according to ASTM E 1921 to ductile cast iron materials was investigated and it was formally used for statistical analysis of ductile cast iron dynamic fracture toughness data. Although the Master curve method was originally introduced for static fracture toughness data of ferritic steels, the successful individual analyses performed here support the engineering way taken to apply the method to ductile cast iron materials too. The results of both methods, the Master curve procedure and the ASME Code Case N-670, show acceptable congruity. At the same time, it is concluded from the present study that further investigations and experiments are required to improve precision and for verification before the results could be applied within component safety analyses.     

A ductile failure model applied to the determination of the fracture toughness of welded joints. Numerical simulation and experimental validation

A ductile-failure model for analysing the fracture behaviour of welded joints has been implemented. Finite element analyses of mismatched welded joints have been performed using the computational cell methodology applied to SE(B) specimens. Different crack lengths, material mismatching, and widths of weld metal have been considered. Ductile parameters have been experimentally and numerically obtained. The influence of geometry and material mismatching on the fracture behaviour of cracked welded joints has been validated by means of a testing program. In addition, the experimental results have been explained through the crack tip constraint, which has been numerically determined.     

Modeling of hydrogen-assisted ductile crack propagation in metals and alloys

This paper presents a finite element study of the hydrogen effect on ductile crack propagation in metals and alloys by linking effects at the microstructural level (i.e., void growth and coalescence) to effects at the macro-level (i.e., bulk material deformation around a macroscopic crack). The purpose is to devise a mechanics methodology to simulate the conditions under which hydrogen enhanced plasticity induces fracture that macroscopically appears to be brittle. The hydrogen effect on enhanced dislocation mobility is described by a phenomenological constitutive relation in which the local flow stress is taken as a decreasing function of the hydrogen concentration which is determined in equilibrium with local stress and plastic strain. Crack propagation is modeled by cohesive elements whose traction separation law is determined through void cell calculations that address the hydrogen effect on void growth and coalescence. Numerical results for the A533B pressure vessel steel indicate that hydrogen, by accelerating void growth and coalescence, promotes crack propagation by linking simultaneously a finite number of voids with the crack tip. This “multiple-void” fracture mechanism knocks down the initiation fracture toughness of the material and diminishes the tearing resistance to crack propagation.     

Calibration procedures for a computational model of ductile fracture

A recent extension of the Gurson constitutive model of damage and failure of ductile structural alloys accounts for localization and crack formation under shearing as well as tension. When properly calibrated against a basic set of experiments, this model has the potential to predict the emergence and propagation of cracks over a wide range of stress states. This paper addresses procedures for calibrating the damage parameters of the extended constitutive model. The procedures are demonstrated for DH36 steel using data from three tests: (i) tension of a round bar, (ii) mode I cracking in a compact tension specimen, and (iii) shear localization and mode II cracking in a shear-off specimen. The computational model is then used to study the emergence of the cup-cone fracture mode in the neck of a round tensile bar. Ductility of a notched round bar provides additional validation.     

Development of stress-modified fracture strain for ductile failure of API X65 steel

The present paper proposes ductile failure criteria in terms of true fracture strain (the equivalent strain to fracture) as a function of the stress triaxiality (defined by the ratio of the hydrostatic stress to the equivalent stress) for the API X65 steel. To determine the stress-modified fracture strain, smooth and notched tensile bars with four different notch radii are tested, from which true fracture strains are determined as a function of the notch radius. Then detailed elastic–plastic, large strain finite element analyses are performed to estimate variations of stress triaxiality in the tensile bars, which leads to true fracture strains as a function of the stress triaxiality, by combining them with experimental results. Two different failure criteria are proposed, one based on local stress and strain information at the site where failure initiation is likely to take place, and the other based on averaged stress and strain information over the ligament where ductile fracture is expected. As a case study, ligament failures of API X65 pipes with a gouge are predicted and compared with experimental data.     

A simple damage-accumulation model for constraint effects on ductile fracture

A simple model is presented to account for the effects of void-type damage on crack initiation and propagation in ductile steels under plane strain conditions by virtue of elementary fracture mechanics solutions. Multiple primary voids from large inclusions are uniformly distributed ahead of the crack tip. The growth of these primary voids is followed by nucleation of a large population of secondary voids from second-phase particles. A critical accumulative damage based on the length ratio of the damage zone to the spacing of primary voids, is employed as a failure criterion, including contributions from two populations of voids. Damage accumulation depends much on the strain and stress states such as stress triaxilities, which are extracted from existing results instead of detailed computation. Results show the dependence of fracture toughness on the size of damage zones associated with constraints. Initiation of crack growth is insensitive to the constraints since nucleation of fine voids is determined by local deformation. The model captures the transition in mechanisms from void-by-void growth to multiple void interactions in terms of a decreasing trend in the slopes of fracture resistance curves. At high constraints and large damage zone, a steady-state crack advance is identified with constant toughness. Damage accumulation from the growth of primary voids determines subsequent crack growth resistance and the study demonstrates its dependences on the crack-tip constraints.     

Gurson model parameters for ductile fracture simulation in ASTM A992 steels

This study is concerned with the modelling the ductile fracture in ASTM A992 steels using the Gurson‐Tvergaard‐Needleman (GTN) model for high stress triaxiality regime. The GTN model for ASTM A992 structural steels is calibrated from the experiments performed on axisymmetrically notched tensile specimens. The experiments are designed to obtain a range of stress triaxiality and different fracture initiation locations. The non‐uniqueness in the constitutive parameters of the GTN model is illustrated in this study. The choice of a unique set of GTN constitutive parameters is made by choosing the nucleation strain (?_N) as a material constant. The process of estimating this material specific nucleation strain is provided. All the other GTN model parameters corresponding to the material specific nucleation strain (?_N) are evaluated to best fit the experimental results. The calibrated GTN model is shown to predict the load displacement behaviour, ductility and fracture initiation locations in the notched specimens. The calibrated GTN parameters are used to successfully predict the ductility of structural components: (a) bars with a hole; (b) plate with reduced section and (c) plate with holes; that are typically found in structural engineering applications.     

A numerical investigation of ductile fracture initiation in a high-strength low-alloy steel

In this work, static and drop-weight impact experiments, which have been conducted using three-point bend fracture specimens of a high-strength low-alloy steel, are analysed by performing finite-element simulations. The Gurson constitutive model that accounts for the ductile failure mechanisms of microvoid nucleation, growth and coalescence is employed within the framework of a finite deformation plasticity theory. Two populations of second-phase particles are considered, including large inclusions which initiate voids at an early stage and small particles which require large strains to nucleate voids. The most important objective of the work is to assess quantitatively the effects of material inertia, strain rate sensitivity and local adiabatic temperature rise (due to conversion of plastic work into heat) on dynamic ductile crack initiation. This is accomplished by comparing the evolution histories of void volume fraction near the notch tip in the static analysis with the dynamic analyses. The results indicate that increased strain hardening caused by strain rate sensitivity, which becomes important under dynamic loading, plays a benign role in considerably slowing down the void growth rate near the notch tip. This is partially opposed by thermal softening caused by adiabatic heating near the notch tip.     

Modelling of ductile fracture initiation in strength mismatched welded joint

In this paper, the effect of strength mismatch and width of the welded joints on the stress–strain distribution in the crack tip region has been discussed. The single-edge notched bend (SENB) specimens (precrack length a₀/W = 0.32) were experimentally and numerically analysed. The model of local approach to fracture, proposed by Gurson, Tvergaard and Needleman, was used. High-strength low-alloyed (HSLA) steel was used as a base metal in quenched and tempered condition. The flux-cored arc-welding process in shielding gas was used. Two different fillers were selected to make over- and undermatched weld metal. The experimental analysis of fracture behaviour of the over- and undermatched welded joints was followed by numerical computations of void volume fraction in front of the crack tip. The critical void volume fraction, f_c, used in prediction of the crack growth initiation on the SENB specimen had been previously determined on a round smooth specimen. Three widths of weld metal were considered: 6, 12 and 18 mm. A comparison of the crack tip opening displacement (CTOD) values corresponding to crack initiation in the SENB specimens is given, as determined both experimentally and using the GTN model.     

舰船结构钢的夏比冲击韧性与断口形貌

论述了从夏比冲击韧性分解出来的断裂扩展功与断口形貌的关系，指出冶金因素对夏比冲击韧性α＿ｋ值和扩展功的影响不完全是一致的，提出采用α＿ｋ，值和断口纤维率作为韧性指标的互补性，建议在我国的舰船结构钢韧性指标中增加断口纤维率的要求。     

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.