Strain-energy density and failure-process zone report 2. Experimental confirmation

Experimental confirmation is presented for a previously obtained, theoretical relationship between the size of the failure-process zone and the total strain-energy density (SED) in dimensionless form for conditions of mixed failure modes under static and cyclic deformation. Characteristic features of subcritical crack growth are delineated for static deformation as a function of type of steel structure. Familiar literature data on the ductile-brittle transition are described, and an equation proposed for calculation of fracture toughness on the basis of standard mechanical properties of materials. Both constraint and scale effects are analyzed for failure under plane stress and plane strain within the framework of the theory under development. Characteristics of cyclic crack growth are compared with fractography data on the fatigue-stria step. It is demonstrated that the results of static and fatigue experiments for steel in different structural compositions lie on one curve common for a given specimen geometry.     

Finite element analysis of creep fracture initiation in a model superalloy material

Detailed finite element analyses were performed for a single edge-cracked specimen geometry under both plane stress and plane strain constraint for a superalloy material that obeys a power-law creep relationship. The objectives of these analyses were to elucidate the stationary creep crack-tip fields and to provide guidance for the experimental measurement of crack-tip deformations. New results demonstrate that, for both plane stress and plane strain, the angular variations in the creep strain fields do not agree with HRR-type predictions, although the radial variations are in agreement with HRR-type creep strain field predictions in a zone very near the crack tip. Thus, the use of experimental measurement of surface displacement and/or strain data for the location of HRR-type fields may not be possible, unless modifications to the existing HRR-type theory are made. It is also noted that the size of the stress-based HRR-dominance zone is only a fraction of the creep zone size in plane stress, and is very small (especially along =0°) compared to the creep zone size in plane strain. Furthermore, the dominance of the singular strain fields are at least two orders of magnitude smaller than the corresponding stress dominance zones. As such, unless the microstructural features of the material are smaller than the dimensions of the dominance zones, the basis for using stress or strain-based fracture parameters derived from the HRR-type fields for prediction of creep fracture initiation is unclear.     

Fracture assessment of Brazilian disc specimens weakened by blunt V-notches under mixed mode loading by means of local energy

The main purpose of this research is to re-analyse experimental results of fracture loads from blunt V-notched samples under mixed mode (I + II) loading considering different combinations of mode mixity ranging from pure modes I to II. The specimens are made of polymethyl-metacrylate (PMMA) and tested at room temperature. The suitability of fracture criterion based on the strain energy density (SED) when applied to these data is checked in the paper. Dealing with notched samples, characterized by different notch angles and notch root radii, the SED criterion used in combination with the concept of local mode I, valid in the proximity of the zone of crack nucleation, permits to provide a simple approximate but accurate equation for the SED in the control volume. This proposal unifies predictions for the experimental results obtained under modes I, II and mixed mode loading.     

Study on coexistence of brittle and ductile fractures in nano reinforcement composites under different loading conditions

Experimental study on high volume fraction of metallic matrix nano composites (MMNCs) was conducted, including uniaxial tension, uniaxial compression, and three-point bending. The example materials were two magnesium matrix composites reinforced with 10 and 15% vol. SiC particles (50 nm size). Brittle fracture mode was exhibited under uniaxial tension and three-point bending, while shear dominated ductile fracture mode (up to 12% fracture strain) was observed under uniaxial compression. The original Modified Mohr–Coulomb (MMC) fracture model (Bai and Wierzbicki in Int J Fract 161:1–20, 2010; in a mixed space of stress invariants and equivalent strain) was transferred into a stress based MMC (sMMC) model. This model was demonstrated to be capable of predicting the coexistence of brittle and ductile fracture modes under different loading conditions for MMNCs. A material post-failure softening model was postulated along the damage accumulation to capture the above two different failure modes. This model was implemented to the Abaqus/Explicit as a material subroutine. Numerical simulations using finite element method well duplicated the material strength, fracture initiation sites and crack propagation modes of the Mg/SiC nano composites with a good accuracy. The proposed model has a good potential to predict fracture for a wide range of material with strength asymmetry and coexistence of brittle and ductile fractures modes.     

The specific enthalpy of fracture for beta Ti-15-3 alloy

Fatigue crack propagation (FCP) experiments were conducted on beta Ti-15-3 alloy under various loading conditions to examine the constancy of the specific enthalpy for fracture, advanced by the Crack Layer (CL) theory as a material parameter characteristic of its intrinsic toughness. The energy release rate and the irreversible work were determined from load-displacement curves during crack propagation. Microscopic and diffraction analyses were conducted to identify the damage mechanisms ahead of the crack tip. A damage zone whose geometry exhibited plane strain character at the initial stage of crack propagation was observed optically. The damage zone transformed into plane stress configuration when the crack reached half its critical length. Damage mechanisms involved slip lines and microcracking which is believed to ensue from intense accumulation of slip processes. The magnitude of microcracking became more weighty as the crack moved deeper into plane stress dominance. The damage preceding crack advance was quantitatively assessed as the crack resistance moment which is the volume of transformed material per unit crack extension. Application of the CL theory to the data generated under a wide range of applied stress levels gave rise to a constant value of the specific enthalpy of fracture, 20 MJ/m³. This value is in close agreement with the specific energy of slip lines computed from microstructural considerations.     

On dual-parameter fracture criterion of welded joints

Based on the existed results of stress field solutions, in the present work a modified dual parameter JQ fracture criterion is proposed for plane strain state, and the criterion may be suitable to both homogeneous material and welded joint. Center cracked welded plate in plane strain condition is selected as a research object. Combined with finite element analysis, discussions are made on the engineering estimate and measurement of the various parameters. The engineering algorithm on the various factors in the fracture criterion is also proposed. Referring to the HRR results, it is indicated that the new criterion can describe stress field nature of homogeneous material and welded joint in plane strain state well. The availability of the new proposed criterion to the homogeneous material and welded joint is discussed. Thereafter, the difficulty of the single parameter J-integral can be overcome, when the modified J-integral parameter is used to describe the stress field intensity of plane strain and weld joint. Thus, the new criterion may be a good basis for engineering evaluation of fracture of welded structures.     

The T-criterion for engineering materials based on strength anisotropy

Summary In most engineering materials the yield limits in tension and compression are in general different. Their ratio,R= _0C / _0T , characterizing the strength anisotropy of the material, was found to influence significantly the modes of both plane stress and plane strain fractures. The theoretical analysis presented in this paper introduced the necessary modifications of theT-criterion of fracture in order to cover the effect of the strength anisotropy, called the strength-differential effect (SDE). According to the statement of the proposed fracture criterion, the maximum value of the ratio of strain energy density components,T _R =T _V /T _D , when calculated along the elastic-plastic boundary around the tip of a crack indicates the angle of initial crack path. Crack onset is characterized by a critical value of the SED. For the determination of the elastic-plastic boundary the most general form of a failure criterion, that is the paraboloid failure condition was used.With 12 Figures     

Averaged strain energy density estimated rapidly from nodal displacements by coarse FE analyses: Cracks under mixed mode loadings

The strain energy density (SED) averaged over a structural volume allows to assess the fracture and fatigue behaviour of cracked components under mixed‐mode loadings. To rapidly estimate the averaged SED, two approaches have been previously proposed: (a) the direct approach; (b) the peak stress method (PSM) and nodal stress (NS) approach. In this paper, the nodal displacement (ND) approach is presented to rapidly estimate the averaged SED from the nodal displacements by FE analyses. This method combines the advantages of all previous approaches, ie, the use of coarse meshes able to capture the contributions of both stress intensity factors (SIFs) and higher order terms, without requiring geometrical modelling of the control volume. To validate the method, cracked plates and cracked bars under mixed‐mode loadings have been analysed. The averaged SED values estimated by the ND approach agree with those calculated by the direct approach, within a range of applicability.     

Experimental determination of the stress-crack opening relation in fibre cementitious composites with a crack-tip singularity

A J-based-fracture-testing method is presented for determining the bridging-stress-crackopening-displacement (-) relationship in fibre-reinforced composites where the crack-tip toughness is not negligible. The J-based technique originally proposed for concrete has been well-established for cementitious composites where the fracture process is primarily dominated by the formation of a fracture-process zone and the contribution of the crack-tip toughness is negligibly small. In this study, the J-based technique is further extended to cover materials for which the crack-tip stress singularity coexists with the fracture-process zone. This extended version of the J-based technique explicitly accounts for the crack-tip singularity while considering the fracture-process zone. This newly derived testing technique has been applied to a high-strength-mortar (HSM) reinforced with carbon and steel fibres where the fibrebridging toughness can be of the same order of magnitude as the crack-tip toughness. The validity of the - relationships deduced has been examined by comparing with results obtained from direct uniaxial tension tests. It is suggested that the J-based-fracture-testing technique can provide reasonable - relationships and fracture parameters in a fibrereinforced HSM.     

The strain-hardening effect in HRR plane fields according to T-criterion

The strain-hardening effect on fracture is investigated with the aid of the T-criterion using HRR stress fields [1–3] around a crack tip in a power hardening material. Using the appropriate components of strain energy density for the elastic-plastic as well as a nearly elastic expression of the T-criterion, we find the fracture angles, as well as fracture stresses in materials possessing an elastic extended up to a perfectly plastic behavior, by considering plane mixed-mode deformation at the crack tip.Significant influence of the strain hardening coefficient, n on the fracture stress, as well as the hardening parameter mainly appeared in plane strain conditions. This phenomenon was observed almost independently of the solution applied, which provides a nearly elastic or an elastic-plastic expression of the T-criterion describing the fracture conditions.     

State‐of‐the‐art review on the local strain energy density concept and its relation to the J‐integral and peak stress method

The local average strain energy density (SED) approach has been proposed and elaborated by Lazzarin for strength assessments in respect of brittle fracture and high‐cycle fatigue. Pointed and rounded (blunt) V‐notches subjected to tensile loading (mode 1) are primarily considered. The method is systematically extended to multiaxial conditions (mode 3, mixed modes 1 and 2). The application to brittle fracture is documented for PMMA flat bar specimens with pointed or rounded V‐notches inclusive of U‐notches. Results for other brittle materials (ceramics, PVC, duraluminum and graphite) are also recorded. The application to high‐cycle fatigue comprises fillet‐welded joints, weld‐like shaped and V‐notched base material specimens as well as round bar specimens with a V‐notch. The relation of the local SED concept to comparable other concepts is investigated, among them the Kitagawa, Taylor and Atzori–Lazzarin diagrams, the Neuber concept of fictitious notch rounding applied to welded joints and also the J‐integral approach. Alternative details of the local SED concept such as a semicircular control volume, microrounded notches and slit‐parallel loading are also mentioned. Coarse FE meshes at pointed or rounded notch tips are proven to be acceptable for accurate local SED evaluations. The peak stress method proposed by Meneghetti, which is based on a notch stress intensity factor consideration combined with a globally even coarse FE mesh and is used for the assessment of the fatigue strength of welded joints, is also presented.     

单调荷载下Q345钢焊缝金属的延性断裂性能研究

为了研究Q345钢焊缝金属的延性断裂性能,对9个试件进行了单调荷载下试验研究,试件设计考虑了不同应力三轴度和洛德角分布范围。分别采用Swift、Voce及Swift-Voce混合强化模型,拟合得到了能预测到断裂时的完整应力-应变曲线,其中Swift-Voce混合强化模型模拟各试件荷载-位移曲线精度最好。采用VGM,改进SWDM和Lou模型3种断裂模型,通过编写UVARM子程序,校准了各模型的材料参数,并对各试件进行了有限元断裂模拟预测,比较分析了各个模型的预测精度。结果表明,VGM模型对接近于平面应变状态的矩形缺口和槽板试件的预测结果误差较大,而改进SWDM和Lou模型通过引入洛德角参数来描述偏应力状态,对不同应力状态的试件断裂预测结果精度更高,模型的适用性更好。     

Cell model for nonlinear fracture analysis – I. Micromechanics calibration

A computational approach based on a cell model of material offers real promise as a predictive tool for nonlinear fracture analysis. A key feature of the computational model is the modeling of the material in front of the crack by a layer of similarly-sized cubic cells. Each cell of size D contains a spherical void of initial volume fraction f ₀. The microseparation characteristics of the material in a cell, a result of void growth and coalescence, is described by the Gurson–Tvergaard constitutive relation; the material outside the layer of cells can be modelled as an elastic- plastic continuum. The success of this computational model hinges on developing a robust calibration scheme of the model parameters. Such a scheme is proposed in this study. The material-specific parameters are calibrated by a two-step micromechanics/fracture-process scheme. This article describes the micromechanics calibration of void growth taking into account both the strain hardening and the strength of the material. The fracture-process calibration is addressed in a companion paper. This revised version was published online in July 2006 with corrections to the Cover Date.     

Impact fracture behaviour of double-base gun propellants

Impact fracture properties of three nitrocellulose—nitroglycerine gun propellants have been measured in a three-point bend mode at moderate impact rates with an instrumented drop-weight impact tester. Dynamic moduli and loss tangents were measured over the temperature range −100 to +120° C, and three transitions were identified. A transition at about −30° C was found to increase the low-temperature fracture toughness of the higher nitroglycerine content propellants. The fracture data were analysed in terms of plane stress and plane strain fracture modes using a simplified model. It was found that the fracture toughness in zones undergoing plastic deformation under plane stress conditions was approximately twice that in zones under plane strain conditions. The plastic zone radii were greater than 0.3 mm at 20° C, falling to about 0.1 mm at −45° C. Strain energy release rates were calculated from fracture load and modulus, and from fracture energy. Good agreement was obtained between the two methods.     

Thickness effect of notched metal sheets on deformation and fracture under tension

The deformation field in notched metal sheets stretched under tension was analysed experimentally. The results of strain distribution were explained by using the result of the near-tip deformation field of non-linear elastic material, combined with a simple model of the plastic state under a mixed plane stress and plane strain condition. Next, the relationship among fracture mechanics parameters, i.e. the notch-tip opening displacement, the notch-tip contraction and $\text{J-}\text{integral}$ was established based on the rigid plastic strip model. Finally, the effect of the specimen thickness on the toughness value at crack initiation and instability was discussed by improving Bluhm's idea that the total fracture resistance was the sum of the fracture work for slant and flat fractures.     

Some aspects of workability studies on P/M sintered high strength 4% Titanium carbide composite steel preforms during cold upsetting

Workability is concerned with the extent to which a material can be deformed in a specific metal working process without the initiation of cracks. Ductile fracture is the most common failure in bulk forming process. The formability is a complicated phenomenon which depends on the friction between the preform and the die surface in cold upsetting. A complete experimental investigation on the workability behavior of the steel composite of 4%TiC was performed under different stress states, namely, plane and triaxial stress state conditions. Cold upsetting of the Fe–1.0%C–4%Ti steel composite preforms was carried out applying different lubricants, namely, graphite, zinc stearate and molybdenum disulphide, and without lubricant, and the formability behaviour of the same under plane and triaxial stress state conditions was determined. The curves plotted for different preforms were analysed and relationship was established between the axial strain and the formability stress index under plane and triaxial state conditions. A relationship between the relative density and the axial strain was also established. Various stress ratio parameters, namely, (σ_θ/σ_eff), (σ_m/σ_eff) and (σ_z/σ_eff), under plane and triaxial stress state conditions were determined empirically as a function of the relative density. An attempt is also made to study the variation of slope of the relative density versus stress ratio parameters under plane and triaxial stress conditions with respect to the relative density to identify the pore closure mechanism.     

Experimental investigation of fracture under controlled stress triaxiality using shear-compression disk specimen

Experimental investigation of the effect of stress triaxiality on fracture strain has been performed using the shear-compression disk (SCD) specimen. A series of experiments was carried out under quasi-static loading conditions at triaxiality levels in the range of \(-\,0.7\) to \(+\,0.05\). The experiments were designed to generate relatively uniform strain and triaxiality in the sheared zone of the specimen, and a constant level of triaxiality along the entire loading path. The results obtained for SAE 1045 steel are compared to previous studies on the same material which revealed considerable differences. Discussion on possible contributing factors to the differences, and the potential of the SCD specimen for fracture investigations are discussed.     

A fracture locus for a 50 volume-percent Al/SiC metal matrix composite at high temperature

The effect of the stress state on the fracture locus function of the 50 vol.% Al/SiC metal matrix composite at high temperature is studied. The value of fracture locus function is quantitatively characterized by the amount of shear strain accumulated prior to the moment of failure. Nondimensional invariant parameters are used as characteristics of the stress state, namely, the stress triaxiality k and the Lode-Nadai coefficient μ _σ showing the form of the stress state. Besides conventional testing for tension, compression and torsion of smooth cylindrical specimens, the complex of mechanical tests includes a new type of testing, namely, that for bell-shaped specimens. These kinds of testing enable one to study fracture strain under monotonic deformation in the ranges μ _σ ?=?0?…?+?1 and k?=???1.08...0 without using high-pressure technologies. The stress–strain state during specimen testing is here evaluated from the finite element simulation of testing in ANSYS. The tests were performed at a temperature of 300 °C and shear strain rate intensity Η?=?0.1;?0.3;?0.5 1/s. The test results have offered a fracture locus, which can be used in models of damage mechanics to predict fracture of the material in die forging processes.     

The form of crack tip plastic zones

The “radius” of the plastic zone at a crack tip is a parameter that has numerous applications in fracture mechanics. However, attention is drawn here to the confusion that is apparent, even in text-books, concerning the calculation of the plastic zone “radius” under plane strain conditions. The aim of this work has been to resolve this point, to determine the actual shape and size of the zone and to investigate the influence of stress state and other factors.The plastic zone dimensions have been simply calculated, over a range of values of Poisson's ratio, for isotropic materials subjected to loading under plane stress and plane strain conditions; the analysis has been further extended to cover some effects of anisotropy. It has been demonstrated that, for isotropic materials, the maximum extent of the plastic zone directly ahead of, and in the plane of, a crack is ($\text{K}{}_{\mathrm{I}}\text{/Y)}{}^2\text{18π}$ under plane stress loading and is ($\text{K}{}_{\mathrm{I}}\text{/Y)}{}^2\text{18π}$ under plane strain loading. This latter result is smaller, by a factor of $\text{1}\text{3}$ than the plastic zone “radius” under plane strain conditions that is widely quoted in fracture mechanics texts. That “radius”, ($\text{K}{}_{\mathrm{I}}\text{/Y)}{}^2\text{6π}$ is, in fact, the maximum size of the zone parallel to, but not in, the plane of the crack, if Poisson's ratio is taken to be $\text{1}\text{3}$.A lower value of Poisson's ratio or an increased material anisotropy can lead to an enlarged plastic zone; this latter conclusion suggests that test-pieces for valid fracture toughness measurements on anisotropic materials could be required to be larger than defined in the relevant British Standard.