Showing papers in "International Journal of Fracture in 2000"

Modes of dynamic shear failure in solids

Abstract: The technique of loading edge cracks by edge impact (LECEI) for generating high rates of crack tip shear (mode-II) loading is presented. The LECEI-technique in combination with a gas gun for accelerating the impactor is used to study the high rate shear failure behaviour of three types of materials. Epoxy resin (Araldite B) shows failure by tensile cracks up to the highest experimentally achievable loading rate; steel (high strength maraging steel X2 NiCoMo 18 9 5) shows a failure mode transition: at low rates failure occurs by tensile cracks, at higher rates, above a certain limit velocity, failure by adiabatic shear bands is observed; aluminum alloy (Al 7075) shows failure due to shear band processes in the high rate regime, but this failure mode is observed over the entire range of lower loading rates, even down to quasi-static conditions. Characteristics of the failure modes are presented. When transitions are observed in the failure process from tensile cracks to shear bands the limit velocity for failure mode transition depends on the bluntness of the starter crack the failure is initiated from: The larger the bluntness of the starter crack the higher the critical limit velocity for failure mode transition. The data indicate that adiabatic shear bands require and absorb more energy for propagation than tensile cracks. Aspects of the energy balance controlling mode-II instability processes in general are considered. Effects very different than for the mode-I instability process are observed: When failure by a tensile crack occurs under mode-II initiation conditions, a notch is formed between the initiated kinked crack and the original starter crack, and, at this notch a compressive stress concentration builds up. The energy for building up this stress concentration field is not available for propagation of the initiated kinked crack. The energy density of a mode-II crack tip stress field, however, when compared to an equivalent mode-I crack tip field, is considerably larger, and, consequently, the remaining driving energy for any mode-II initiated failure process, nevertheless, is higher than for the case of equivalent mode-I initiation conditions. Furthermore, mode-II crack tip plastic zones are considerably larger than equivalent mode-I crack tip plastic zones. Consequently, validity conditions for linear-elastic or small scale yielding failure behaviour are harder to fulfill and possibilities for the activation of nonlinear high energy ductile type failure processes are enhanced. Speculations on how these effects might favour failure by high energy processes in general and by shear bands processes in particular for conditions of high rate shear mode-II loading are presented.

Numerical Calculation of Stress Intensity Factors in Functionally Graded Materials

Abstract: The finite element method is studied for its use in cracked and uncracked plates made of functionally graded materials. The material property variation is discretized by assigning different homogeneous elastic properties to each element. Finite Element results are compared to existing analytical results and the effect of mesh size is discussed. Stress intensity factors are calculated for an edge-cracked plate using both the strain energy release rate and the J-contour integral. The contour dependence of J in an inhomogeneous material is discussed. An alternative, contour independent integral $$\tilde J$$ is calculated and it is shown numerically that $$\tilde J$$ , the strain energy release rate G, and the limit of J as Γ approaches the crack tip (where Γ is the contour of integration) are all approximately equal. A simple method, using a relatively coarse mesh, is introduced to calculate the stress intensity factors directly from classical J-integrals by obtaining lim#x0393;→ 0 J.

Buckling and cracking of thin films on compliant substrates under compression

Abstract: It is shown that unless the substrate is at least as stiff as the film, the energy stored in the substrate contributes significantly to the energy release rate of film delamination under compression either with or without cracking. For very compliant substrates, such as polyethylene terephthalate (PET) with a indium tin oxide (ITO) film, the energy release rate allowing for the deformation of the substrate can be more than an order of magnitude greater than the value obtained neglecting the substrate's deformation. The argument that buckling delaminations tunnel at the tip rather than spread sideways because of increase in mode-mixity may need modification; it is still true for stiff substrates, but for compliant substrates the average energy release rate decreases with delamination width and the limitation in buckled width may be due to this stability as much as the increase in mode-mixity.

A simplified method for determining double-K fracture parameters for three-point bending tests

Abstract: A simplified method for determining the double-K fracture parameters K Ic ini and K Ic un for three-point bending tests is proposed. Two empirical formulae are used to describe the crack mouth opening displacement CMOD and the stress intensity factor K I c caused by the cohesive force σ(x) on the fictitious crack zone for three-point bending beams. It has been found that the two empirical formulae are accurate for a large practical region of a/D. Experiments carried out by many researchers showed that the new formula of CMOD for three-point bending beams can be directly used to predict the initial crack length for precracked beams, the notch depth and the critical effective crack length, as well as the crack length in the post-critical situation with a satisfactory accuracy. Further verification is demonstrated to determine the double-K parameters K Ic ini and K Ic un. They are very close to those determined by the method proposed in our previous work. Using the simplified procedure, the experiments can be performed even without a closed-loop testing facility and the calculation can be carried out on a pocket calculator.

Fracture mechanics analysis of a crack in a residual stress field

Abstract: The standard definition of the J integral leads to a path dependent value in the presence of a residual stress field, and this gives rise to numerical difficulties in numerical modelling of fracture problems when residual stresses are significant. In this work, a path independent J definition for a crack in a residual stress field is obtained. A number of crack geometries containing residual stresses have been analysed using the finite element method and the results demonstrate that the modified J shows good path-independence which is maintained under a combination of residual stress and mechanical loading. It is also shown that the modified J is equivalent to the stress intensity factor, K, under small scale yielding conditions and provides the intensity of the near crack tip stresses under elastic-plastic conditions. The paper also discusses two issues linked to the numerical modelling of residual stress crack problems-the introduction of a residual stress field into a finite element model and the introduction of a crack into a residual stress field.

Predicting the service-life of adhesively-bonded joints

Abstract: A fracture-mechanics approach has been used to predict the cyclic-fatigue performance of the adhesively-bonded single-lap joint and a typical bonded component, represented by an adhesively-bonded `top-hat' box-beam joint The joints were tested under cyclic-fatigue loading in either a `wet' or `dry' environment, respectively Several steps were needed to predict the cyclic-fatigue lifetime of these joints Firstly, fracture-mechanics tests were used to obtain the relationship between the rate of fatigue crack growth per cycle, da/dN, and the maximum strain-energy release-rate, Gmax, applied during the fatigue cycle for the adhesive/substrate system under investigation, in both a `dry' and a `wet' test environment Secondly, analytical and finite-element theoretical models were developed to describe the variation of the strain-energy release-rate with crack length, as a function of the applied fatigue loads, for the single-lap joint and the `top-hat' box-beam joint Thirdly, the experimental results from the short-term fracture-mechanics tests, obtained under similar test conditions and in the same environment as were used for the single-lap or bonded box-beam joints, were combined with the modelling results from the theoretical studies This enabled the cyclic-fatigue performance of the single-lap or bonded box-beam joints to be predicted over relatively long time-periods Finally, the agreement between the theoretical predictions and the experimentally-measured cyclic-fatigue behaviour for the joints was found to be very good

Modelling the fracture of concrete under mixed loading

Abstract: A simple and efficient numerical procedure for mixed mode fracture of quasibrittle materials is shown: This technique predicts crack trajectories as well as load-displacement or load-CMOD responses The model is based on the cohesive crack concept and uses the local mode I approach Numerical results agree quite well with three experimental sets of mixed mode fracture of concrete beams; one from Arrea and Ingraffea, another from Garcia, Gettu and Carol and from a nonproportional loading by the authors In constrast to more sophisticated models, this method offers two major advantages: it requires only material properties measured by standardized methods and it can easily be implemented with general multipurpose finite element codes

Failure mode transition in ceramics under dynamic multiaxial compression

Abstract: An experimental technique based on the Kolsky pressure bar has been developed to investigate the behavior of ceramics under dynamic multiaxial compression. Experimental results for aluminum nitride (AlN), together with data available in the literature, indicate that a Mohr-Coulomb criterion and the Johnson–Holmquist model fit the experimental data for failure in a brittle manner, whereas the ceramic material exhibited pressure insensitive plastic flow at high pressures. A failure surface is constructed which represents the material failure behavior, including brittle failure, brittle/ductile transition and plastic flow, under various pressures. The effect of various material properties on the failure behavior was investigated. The Poisson's ratio is found to be a measure of brittleness for ceramic materials with low spall strength under shock wave loading conditions. Lower value of Poisson's ratio indicates that the material will fail in a brittle manner through axial splitting even under uniaxial strain loading; whereas materials with higher Poisson's ratio may be expected to deform plastically beyond the Hugoniot Elastic Limit (HEL). The applicability of the proposed failure surface to a range of ceramics is explored and the limitations of the model are outlined.

Constraint effects on the ductile-to-brittle transition temperature of ferritic steels: a Weibull stress model

Abstract: This study examines crack front length and constraint loss effects on cleavage fracture toughness in ferritic steels at temperatures in the ductile-to-brittle transition region A local approach for fracture at the micro-scale of the material based on the Weibull stress is coupled with very detailed three-dimensional models of deep-notch bend specimens A new non-dimensional function g(M) derived from the Weibull stress density describes the overall constraint level in a specimen This function remains identical for all geometrically similar specimens regardless of their absolute sizes, and thus provides a computationally simple approach to construct (three-dimensional) fracture driving force curves σw vs J, for each absolute size of interest Proposed modifications of the conventional, two-parameter Weibull stress expression for cumulative failure probability introduce a new threshold parameter σw−min This parameter has a simple calibration procedure requiring no additional experimental data The use of a toughness scaling model including σw−min>0 increases the deformation level at which the CVN size specimen loses constraint compared to a 1T SE(B) specimen, which improves the agreement of computational predictions and experimental estimations Finally the effects of specimen size and constraint loss on the cleavage fracture reference temperature T 0 as determined using the new standard ASTM E1921 are investigated using Monte Carlo simulation together with the new toughness scaling model

A method for dynamic fracture toughness determination using short beams

Abstract: This paper deals with dynamic fracture toughness testing of small beam specimens. The need for testing such specimens is often dictated by the characteristic dimensions of the end product. We present a new methodology which combines experimentally determined loads and fracture time, together with a numerical model of the specimen. Calculations are kept to a minimum by virtue of the linearity of the problem. The evolution of the stress intensity factor (SIF) is obtained by convolving the applied load with the calculated specimen response to unit impulse force. The fracture toughness is defined as the value of the SIF at fracture time. The numerical model is first tested by comparing numerical and analytical solutions (Kishimoto et al., 1990) of the impact loaded beam. One point impact experiments were carried out on of commercial tungsten base heavy alloy specimens. The robustness of the method is demonstrated by comparing directly measured stress intensity factors with the results of the hybrid experimental-numerical calculation. The method is simple to implement, computationally inexpensive, and allows testing of large sample sizes, without restriction on the specimen geometry and type of loading.

Evaluation of energy release rate-based approaches for predicting delamination growth in laminated composites

Abstract: A variety of energy release rate-based approaches are evaluated for their accuracy in predicting delamination growth in unidirectional and multidirectional laminated composites. To this end, a large number of unidirectional and multidirectional laminates were tested in different bending and tension configurations. In all cases, the critical energy release rate was determined from the tests in the most accurate way possible, such as by compliance calibration or the area method of data reduction. The mode mix from the tests, however, was determined by a variety of different approaches. These data were then examined to determine whether any of the approaches yielded the result that toughness was a single-valued function of mode mix. That is, for an approach to have accurate predictive capabilities, different test geometries that are predicted to be at the same mode mix must display the same toughness. It was found that variously proposed singular field-based mode mix definitions, such as the β=0 approach or basing energy release rate components on a finite amount of crack extension, had relatively poor predictive capabilities. Conversely, an approach that used a previously developed crack tip element analysis and which decomposed the total energy release rate into non-classical components was found to have excellent predictive capabilities. It is postulated that this approach is more appropriate for many present-day laminated composites.

A note on fracture criteria for interface fracture

Abstract: Several criteria for interface fracture are examined and compared to test results obtained from glass/epoxy specimens. These include two energy release rate criteria, a critical hoop stress criterion and a critical shear stress criterion. In addition, approximate plastic zone size and shape within the epoxy are determined for these tests.

Mixed Mode Fracture in Plain and Reinforced Concrete: Some Results on Benchmark Tests

Abstract: Three different models for concrete based on local and non-local approaches have been adopted to investigate the mechanical behaviour of plain and reinforced concrete when undergoing mixed-mode fracture. The purpose of the research is to understand the results of some benchmark tests, to compare the models with each other and with experiments, and to estimate the reliability of the modelling. To create a sound basis for the comparison, the discretizations, the boundary conditions and the material data are considered, when possible, as unified parameters for the different models in each benchmark test.

Crack Growth analysis of plates Loaded by bending and tension using dual boundary element method

Abstract: This paper presents an extension of the dual boundary element method to analysis of crack growth in plates loaded in combine bending and tension. Five stress intensity factors, two for membrane behaviour and three for shear deformable plate bending are computed using the J-Integral technique. Crack growth processes are simulated with an incremental crack extension analysis based on the maximum principal stress criterion. The method is considered effective since no remeshing is required and the crack extension is modelled by adding new boundary elements to the previous crack boundaries. Several incremental crack growth analysis for different configurations and loadings are presented.

Failure mode transitions in polymers under high strain rate loading

Abstract: A rather unusual failure mode transition from brittle to ductile at high strain rates occurs under a combined pressure and shear loading. This transition also represents a change in the failure mode from a normal stress dominated fracture mode at low loading rates to a shear stress dominated shear banding failure at high strain rates. While most such observations have been in metallic materials, where such transitions are attributed to thermal softening caused by adiabatic heating, in this paper we present evidence of such mode transitions in a polymer. Experimental observations of the pressure-shear loading experiments are reported in two polymers; polycarbonate (PC) and polymethylmethacrylate (PMMA). Dynamic photomechanics techniques were used in obtaining information regarding the crack tip state in these experiments. While PC exhibits a failure mode transi- tion to shear banding, PMMA changes to a shear mode of fracture; dynamic shear fracture has been observed in real-time using high speed photography for the first time. A numerical simulation of the experiment using a simple constitutive description of the material is performed in order to gain an understanding of the evolution of the crack tip fields that generate the observed mode transitions. The results of the simulation suggest that thermal softening may not play a significant role in the failure mode transitions in polymers. On the other hand, it is shown that the competition between shear yielding and normal stress dominated fracture mechanisms is the key to the failure mode transitions in these polymers.

Crack patterns in brittle thin films

Abstract: The physical system studied is a brittle elastic film bonded to an elastic substrate with different elastic properties; a residual tensile stress is presumed to exist in the film. The focus of the study is the influence of the mismatch in elastic properties on patterns of crack formation in the film. The stress intensity factor and crack driving force for growth of a periodic array of cracks in the direction normal to the interface under two-dimensional conditions are determined for any crack depth and any mismatch in elastic parameters. It is found that, even for a relatively stiff film material, the stress intensity factor of each crack as a function of crack depth exhibits a local maximum. The driving force for crack extension in the direction parallel to the interface is then determined on the basis of these two-dimensional results, and the equilibrium spacing of crack arrays is estimated for given residual stress. The results of the calculations are used as a basis for qualitative arguments to explain the crack patterns which have been observed in GaN films on Si substrates.

Characteristics of three-dimensional stress fields in plates with a through-the-thickness crack

Abstract: Three-dimensional finite element analyses were performed on plates with a through-the-thickness crack. Global-local finite element technique with sub-modeling was used to achieve the refinement required to obtain an accurate stress field. The existence of a weaker singularity was verified, and a model was proposed to explain the behavior of stresses in the boundary layer. This model is able to account for the competing interaction between the inverse square root singular term and the vertex singular term. The energy release rate was calculated using the modified crack closure method and energy balance. A simple technique without 3-D calculation was suggested for evaluating an approximate 3-D stress intensity factor at the mid-plane. The effect of plate thickness on the size of the three-dimensional region was studied, and the validity of two-dimensional linear elastic fracture mechanics was discussed.

An anisotropic Gurson type model to represent the ductile rupture of hydrided Zircaloy-4 sheets

Abstract: The aim of this work is to model the ductile fracture of Zircaloy-4 sheets containing various amount of embrittling hydride precipitates. The proposed model is based on the Gurson–Tvergaard–Needleman model which is extended to take into account plastic anisotropy and viscoplasticity. The mechanical behavior is identified by conducting tensile tests and the damage nucleation rate (hydride cracking) is measured using quantitative metallography. The model is then used in a Finite Element software to represent crack propagation in Center Crack Panel specimens. Results are strongly mesh size dependent. The mesh size has to be identified by comparison with experimental results. Finally the model is validated by simulating crack initiation and growth in moderately complex structures (sheets containing holes).

Exact and variational theorems for fracture mechanics of composites with residual stresses, traction-loaded cracks, and imperfect interfaces

Abstract: By partitioning the total stresses in a damaged composite into either mechanical and residual stresses or into initial and perturbation stresses, it was possible to derive several exact results for the energy release rate due to crack growth. These general results automatically include the effects of residual stresses, traction-loaded cracks, and imperfect interfaces. The exact energy release rate results were expressed in terms of exact solutions to reduced composite stress analysis problems. By considering the common situation where the initial stresses are known exactly, but the perturbation stresses are only known approximately, it was possible to derive rigorous upper and lower bounds to the energy release rate for crack growth. Some of the new fracture mechanics equations were applied to crack closure calculations, to fiber fracture and interfacial debonding in the fragmentation test, and to microcracking in composite laminates.

Finite element analysis of micromechanical failure modes in a heterogeneous ceramic material system

Abstract: A micromechanical model that provides explicit accounts for arbitrary microstructures and arbitrary fracture patterns is developed and used. The approach uses both a constitutive law for the bulk solid constituents and a constitutive law for fracture surfaces. The model is based on a cohesive surface formulation of Xu and Needleman and represents a phenomenological characterization for atomic forces on potential crack/microcrack surfaces. This framework of analysis does not require the use of continuum fracture criteria which assume, for example, the existence of K-fields. Numerical analyses carried out concern failure in the forms of crack propagation and microcrack formation. Actual microstructures of brittle alumina/titanium diboride (Al2O3/TiB2) composites are used. The results demonstrate the effects of microstructure and material inhomogeneities on the selection of failure modes in this material system. For example, the strength of interfaces between the phases is found to significantly influence the failure characteristics. When weak interfacial strength exists, interfacial debonding and microcrack initiation and growth are the principal mode of failure. When strong interfacial strength is derived from material processing, advancement of a dominant crack and crack branching are observed.

Identification of Gurson-Tvergaard material model parameters via Kalman filtering technique. I. Theory

Abstract: In this paper quasi-static ductile fracture processes are simulated within the framework of the finite element method by means of the Gurson–Tvergaard isotropic constitutive model for progressively cavitating elastoplastic solids The progressive degradation of the material strength properties in the fracture process zone due to micro-void growth to coalescence is modeled through the computational cell concept Among the several model parameters to be calibrated in the computations, attention is restricted to the Tvergaard coefficients q1 and q2 and to the initial porosity f0 in the unstressed configuration To identify these model parameters the inverse problem is solved via the extended Kalman filter for nonlinear systems coupled to a numerical methodology for the sensitivity analysis In part I of this work the theory of Kalman filtering and sensitivity analysis is presented First results concerning the identification of the Tvergaard parameters for a whole crack growth in single edge notched bend specimens made of a pressure vessel steel are presented In order to enhance the convergence towards the final solution of the identification procedure, during the tests measurements are made of the displacements of points located in the central portion of the notched specimens, where model parameters highly affect the system state variables In part II of this work a numerical validation of the proposed procedure in terms of uniqueness of the final identified solution, requirements of accuracy for the Bayesian initialization of the model parameters and sensitivity to the experimental measurement errors will be presented and discussed

Determination of energy release rate and mode mix in three-dimensional layered structures using plate theory

Abstract: A plate theory-based method for determining energy release rates is presented for general loadings of three dimensional layered structures. Mode decomposition is performed for cases that exhibit an inverse square root singularity and for which certain other restrictions apply. Predictions for energy release rate and mode mix for typical problems are presented and verified by comparison with results obtained by three dimensional finite element analyses.

Constraint-modified J−R curves and its application to ductile crack growth

Abstract: The concept of J-controlled crack growth is extended to J−A 2 controlled crack growth using J as the loading level and A 2 as the constraint parameter. It is shown that during crack extension, the parameter A 2 is an appropriate constraint parameter due to its independence of applied loads under fully plastic conditions or large-scale yielding. A wide range of constraint level is considered using five different types of specimen geometry and loading configuration; namely, compact tension (CT), three-point bend (TPB), single edge-notched tension (SENT), double edge-notched tension (DENT) and centre-cracked panel (CCP). The upper shelf initiation toughness J IC, tearing resistance T R and J−R curves tested by Joyce and Link (1995) for A533B steels using the first four specimens are analysed. Through finite element analysis at the applied load of J IC, the values of A 2 for all specimens are determined. The framework and construction of constraint-modified J−R curves using A 2 as the constraint parameter are developed and demonstrated. A procedure of transferring the J−R curves determined from standard ASTM procedure to non-standard specimens or practical cracked structures is outlined. Based on the test data, the constraint-modified J−R curves are presented for the test material of A533B steel. Comparison shows the experimental J−R curves can be reproduced or predicted accurately by the constraint-modified J−R curves for all specimens tested. Finally, the variation of J−R curves with the size of test specimens is produced. The results show that larger specimens tend to have lower crack growth resistance curves.

Three-dimensional numerical simulation of the Kalthoff experiment

Abstract: We use the finite element code DYNA3D to analyze large thermomechanical deformations of a prenotched plate impacted on the notched side by a cylindrical projectile moving parallel to the axis of the notch. Both the projectile and the plate are assumed to be made of the same thermally softening but strain and strain-rate hardening material. It is found that the maximum speed imparted to points of the plate on the impact surface equals nearly 90% of the projectile speed, and the rise time depends upon the quasistatic yield stress of the material. Whereas deformations on the midsurface of the plate closely resemble a plane strain state of deformation, those on the traction free front and back surfaces are quite different. Thus measurements made on these surfaces may not describe well the deformations occurring in the interior of the plate.

A tensile strength model for unidirectional fiber-reinforced brittle matrix composite

Abstract: A model for the ultimate tensile strength of unidirectional fiber-reinforced brittle matrix composite is presented. In the model, transverse matrix crack spacing and change in debonding length between the fiber and the matrix is continuously monitored with increasing applied load. A detailed approximate stress analysis, together with a Weibull failure statistics for fiber fracture, are used to determine the probability of fiber fracture and fiber fracture location in the composite. Results of the model are consistent with experimental data. It is suggested from the results that the strength and toughness of the composite are significantly influenced by the Weibull modulus of the fiber and the fiber/matrix interfacial shear stress. A higher fiber Weibull modulus results in a lower composite strength while a higher fiber/matrix interfacial shear stress results in a composite with higher strength but lower toughness. A moderate variation in matrix strength and fiber/matrix interfacial shear strength does not significantly affect the strength of the composite.

Numerical modeling of the ductile-brittle transition

Abstract: Numerical studies of the ductile-brittle transition are described that are based on incorporating physically based models of the competing fracture mechanisms into the material's constitutive relation. An elastic-viscoplastic constitutive relation for a porous plastic solid is used to model ductile fracture by the nucleation and subsequent growth of voids to coalescence. Cleavage is modeled in terms of attaining a temperature and strain rate independent critical value of the maximum principal stress over a specified material region of the order of one or two grain sizes. Various analyses of ductile-brittle transitions carried out within this framework are discussed. The specimens considered include the Charpy V-notch test and cracked specimens under mode I or mode II loading conditions. The fracture mode transition emerges as a natural outcome of the initial-boundary value problem solution.

A practical testing approach to determine mode II fracture energy GIIF for concrete

Abstract: Continuing the experiments on the double-edge notched specimens on which the mode II fracture toughness KIIc of concrete was measured, a practical testing approach to determine mode II fracture energy GIIF is studied using the same geometry.

Correlations among dynamic stress intensity factor, crack velocity and acceleration in brittle fracture

Abstract: Dynamic fracture in PMMA was studied to determine the correlations among dynamic stress intensity factor KID, crack velocity \( \dot a \) and acceleration a. Specimen geometry, a single-edge-cracked tensile plate with two circular holes, was employed to obtain the crack acceleration, deceleration and re-acceleration process in a single fracture event. KID was evaluated using the method of caustics in combination with a Cranz-Schardin high-speed camera and correlated with \( \dot a \) and a. The behaviors of KID\( \dot a \) and a in a SEN specimen were also examined, and the following correlations were obtained: (1) KID was an increasing function of \( \dot a \), but their relation was not unique. (2) KID for a constant velocity \( \dot a \) was larger when the crack was decelerated than when it was accelerated. (3) KID was dependent on both \( \dot a \) and a, and KID for a=constant could be uniquely related to \( \dot a \).

A numerical study of the elastic stress field arising from sharp and blunt V-notches in a SENT-specimen

Abstract: The elastic stress field arising from a V-notch in a Single Edge Notched Tension (SENT) specimen is studied using the Sherman–Lauricella integral equation. Accurate values of the generalized stress intensity factor, here denoted QI, are determined and compared with values from the literature. A QI-dominated distance ahead of the notch tip is defined and determined for several notch angles and different notch depth to specimen width ratios. It is found that for depth to width ratios over 0.45 the QI-dominated distance is approximately constant while below this value the distance can show a great variation with the notch angle. Additionally, a general formula for the maximum stress in a V-notch with a finite root radius is derived. Its applicability on the SENT-specimen is studied and presented as a family of curves. If used within these curves, the formula can accurately predict stress concentrations, even for very smooth notches.

The separation of the fracture energy in metallic materials

Abstract: The total plastic strain energy which is consumed during fracture of a plain-sided CT specimen is separated into several components These are the energies required for deforming the specimen until the point of fracture initiation, for forming the flat-fracture surfaces, for forming the shear-lip fracture surfaces, and for the lateral contraction and the blunting at the side-surfaces, W lat Characteristic crack growth resistance terms, R flat and R slant, are determined describing the energies dissipated in a unit area of flat-fracture and slant-fracture surface, respectively R flat is further subdivided into the term R surf, to form the micro-ductile fracture surface, and into the subsurface term, R sub, which produces the global crack opening angle Two different approaches are used to determine the fracture energy components The first approach is a single-specimen technique for recording the total crack growth resistance (also called energy dissipation rate) Plain-sided and side-grooved specimens are tested The second approach rests on the fact that the local plastic deformation energy can be evaluated from the shape of the fracture surfaces A digital image analysis system is used to generate height models from stereophotograms of corresponding fracture surface regions on the two specimen halves Two materials are investigated: a solution annealed maraging steel V 720 and a nitrogen alloyed ferritic-austenitic duplex steel A 905 For the steel V 720 the following values are measured: J i=65 kJ/m2, R surf=20 kJ/m2, R flat=280 kJ/m2, R slant=1000 kJ/m2, W lat=30 J For the steel A 905 which has no shear lips, the measured values are: J i=190 kJ/m2, R flat=1000 kJ/m2, and W lat=45 J Apart from materials characterization, these values could be useful for predicting the influence of specimen geometry and size on the crack growth resistance curves Key words: Elastic-plastic fracture mechanics, fracture energy, energy dissipation rate, fracture surface analysis