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.     

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.     

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 micromechanical constitutive model for dynamic damage and fracture of ductile materials

This paper proposes a detailed theoretical analysis of the development of dynamic damage in plate impact experiments for the case of high-purity tantalum. Our micro-mechanical model of damage is based on physical mechanisms (void nucleation and growth). The model is aimed to be general enough to be applied to a variety of ductile materials subjected to high tensile pressure loading. In this respect, the work of Czarnota et al. (J Mech Phys Solids 56:1624–1650, 2008) has been extended by introducing the concept of nucleation law and by entering a nonlinear formulation of the elastic response based on the Mie-Grüneisen equation of state. This later aspect allows us to consider high impact velocities. All model parameters are directly assessed by experimental measurements to the exception of the nucleation law which is characterized by the way of an inverse identification method using three free-surface velocity profiles (at low, intermediate and high impact velocities). It is shown that the nucleation law can be consistently determined in the range of operating pressures. The nucleation law being identified, the development of internal damage happens to be a natural outcome of the modelling. The model is applied to predict damage development and free-surface velocity profiles for various test conditions. The variety and the quality of results support the physical basis (in particular micro-inertia effects) upon which the proposed model of dynamic damage is based.     

A theoretical approach for evaluating the plane strain fracture toughness of ductile metals

Fracture Mechanics of Ductile Metals (FMDM) theory is used to obtain the plane strain fracture toughness, K_lc, for different materials. The traditional approach for obtaining the K_lc value is to conduct several standard tests on cracked plates that are costly and time consuming. The fracture toughness value provided by the FMDM theory depends on the stress-strain curve for the material in question, and this is readily available in MIL-HDBK-5 and other reliable sources. The results of the plane strain fracture toughness (K_lc) values provided by the FMDM theory were compared with the experimental data and it was concluded that the two are in excellent agreement. It is proposed that, in the interest of economy and convenience, K_lc testing could be replaced by the FMDM theory.     

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.     

The role of inclusions in ductile fracture and fracture toughness

Electron microscopical examination of fracture surfaces and micro-structures of thirteen different aluminium alloys revealed that ductile rupture is initiated at small inclusions. The average dimple spacing is equal to the average inclusion distance.Void initiation is probably the critical event in ductile fracture; it is immediately followed by spontaneous growth and coalescence of the voids. A dislocation model is developed compatible with this point of view. Evaluation of this dislocation model yields a relation between the fracture strain and the volume fraction of the inclusions.     

On a relationship between stretched zone parameters and fracture toughness of ductile structural steels

Quantitative stereofractographic analysis of the stretched zone at the crack tip is performed on specimens of two ductile steels used for determining fracture toughness. The effect of temperature, loading rate, stress-state mode and specimens size on the stretched zone formation is studied. A correlation is obtained of the stretched-zone height and width with fracture toughness of materials and the crack tip opening displacement value which is determined by means of various mathematical models.     

The measurements of fracture toughness of ductile materials

Near tip strain is proposed as a ductile fracture criterion. This criterion was used to study the onset of slow growth of surface crack. The data from two batches, B and C, of fully annealed 2024-0 aluminum alloy and HY-80 steel substantiated the proposed criterion. The measured fracture toughness at the onset of surface crack growth are 280, 110 and 800 ksi √in. for these three materials respectively. It was demonstrated that the measurement can be made easily with a small foil resistance strain gage. The near tip strain criterion was compared with both crack surface opening displacement and J-integral criteria.     

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.     

Statistical scatter of fracture toughness in the ductile-brittle transition of a structural steel

The statistical scatter of fracture toughness in the ductile-brittle transition temperature range was experimentally examined on a 500 MPa class low carbon steel. Fracture toughness tests were replicatedly performed at −60 °C, −20 °C and −10 °C. The tests at −60 °C resulted in a single modal Weibull distribution with a shape parameter of 4 for the critical stress intensity factor converted from J-integral, whereas the Weibull distributions of the critical stress intensity factor at −20 °C and −10 °C showed a bilinear pattern with an elbow point, which caused a wider scatter than that at −60 °C. Such scatter transition behavior was discussed with reference to stable crack initiation. A model of the statistical scatter transition has been proposed in this work and the model reasonably explains the experimental results.     

Determination of dynamic fracture toughness for PMMA

A dynamic FEM (finite element method) and a strain gage method are applied to analyze the dynamic fracture toughness and SIF (stress intensity factor) for PMMA (polymethyl methacrylate). The analyses are carried out for plates with an edge crack subjected to one-point bending in a plane of the plate. A simple procedure that the present author has proposed is applied to the problem of using a triangular element of assumed constant strain on finite element analysis. The numerical simulation by FEM provides values for the applied forces as measured with the strain gages. Also, a crack initiation time is measured with the strain gage mounted around the crack tip. The dynamic fracture toughness is determined by adapting the crack initiation time to the simulation curve of the dynamic SIF calculated by the FEM. In this study, the usefulness of the method to determine the dynamic fracture toughness is investigated by comparing predictions with the experimental results for dynamic stresses and SIFs.     

An assessment of fracture toughness in the ductile to brittle transition regime using the Euro fracture toughness dataset

The effect of specimen size on the fracture toughness of a ferritic steel in the transition regime has been investigated in a joint European Project. The project involved the testing of 25, 50, 100 and 200 mm wide compact specimens over the temperature range −154°C to 20°C with the aim of evaluating techniques for assessing the fracture toughness data.This paper evaluates the data at, or close to, the onset of stable tearing instead of at cleavage. The approach, which is applicable to structural assessment procedures, results in a temperature shift of less than 12°C between the specimen widths. The approach also enables simplified recommendations to be made for fracture toughness testing in the transition regime and the onset of upper shelf behaviour to be quantified.     

Controlling fracture toughness of matrix for ductile fiber reinforced cementitious composites

An experimental study was carried out to find material parameters for making fiber reinforced cementitious composites (FRCC) more ductile. One of the dominant factors to control the ductility might be hidden in fracture property of matrix as well as the interface property between fiber and matrix. Therefore this study varied air content and water-binder ratio as the parameters to change the fracture property of matrix and experimentally examined their influence on the ductility of FRCC by three-point bend test with notched beams. As a result, it is concluded that fracture toughness of the matrix could be one of key parameters to control the ductility of FRCC. In case of a polyethylene fiber used in this study, the optimum value of the fracture toughness (critical strain energy release rate): G_IC of the matrix was obtained to be 7.5-8.0 N/m.