Stress-based Fracture Criterion Research Articles

Characterization and modelling of evolving plasticity behaviour up to fracture for FCC and BCC metals

Yield surfaces evolve depending on loading directions (anisotropic hardening) and stress states (differential hardening) during plastic deformation of sheet metals. A new analytical yield function is proposed by coupling an enhanced pDrucker function and SY2009 anisotropic hardening functions to model both the differential and anisotropic hardening behavior. All the parameters are solved analytically for the proposed function so that the proposed function can model the differential hardening from uniaxial compression to equibiaxial tension and anisotropic hardening of uniaxial tension with three different loading directions. Its convexity during evolution is analysed from plasticity onset to ultimate fracture by a geometry-inspired numerical convex analysis approach. Several tests were conducted for an aluminium alloy 2A12-O and a high-strength steel QP1180 including uniaxial tension/compression, simple shear, notched tension and bulge tests. The proposed yield function is applied to describe the plastic behaviour of AA2A12-O and QP1180 steel under the non-associated flow rule. Parameter calibration is conducted at pre-necking and post-necking stages for modelling yield surface evolution more accurately under large deformation especially at shear and equibiaxial tension states. The applications to the two metals show that the proposed function is more suitable for pressure-sensitive face-centered cubic (FCC) and body-centered cubic (BCC) metals compared to the pressure-coupled Yld2000–2d and CQN models since both the anisotropic and differential hardening behaviours are precisely modelled by the proposed yield function. The proposed function could also be utilized as a stress-based fracture criterion to model four stress states fracture from uniaxial compression to equibiaxial tension.

The applicability and the low limit of the classical fracture theory at nanoscale: The fracture of graphene

Miniaturization of mechanical structures offers excellent performances of the device while has brought problems of fracture at nanoscale. However, whether the classical fracture theory is applicable at such a small scale and what is its low limit are still challenging problems. In this paper, by conducting atomistic simulation of graphene and compared with the reported in-situ experiments, the applicable range of distance from crack tip for crack-tip stress distribution models and the low limit of crack length for fracture criterion are investigated. It is found that all crack-tip stress models are invalid within fracture process zone whose dimension is 2.5 Å away from crack tip. The energy-based fracture criteria are not applicable when the crack length is less than 8 nm due to the nonlinear stress–strain relationship, while the modified Griffith criterion can be applied to low limit of crack length 5 Å. For the stress-based fracture criterion, the stress intensity factor criterion fails when the crack length is less than 8 nm due to the decreasing size of critical K-dominant zone ΛK, while the theory of critical distances and quantized fracture mechanics can accurately predict the critical fracture stress regardless of the crack length, which can be unified by a non-local stress criterion. This work will provide a mechanical basis for the reliable application of the microelectronic devices at nanoscale.

On the use of Brazilian disk specimen for measuring mixed-mode I/II translaminar fracture toughness of notched glass/epoxy composite laminates: A comprehensive study

In this work, a comprehensive experimental and theoretical study is performed on laminated composites containing V- and U-notch to evaluate the last-ply-failure (LPF) load in mixed-mode I/II loading conditions. Numerous tests are conducted on the composite laminates using the Brazilian disk specimen for the first time. The samples are fabricated of E-glass/epoxy in three different lay-up configurations, namely unidirectional, cross-ply, and quasi-isotropic. Three notch opening angles of 2α = 30°, 60°, and 90° are considered for the V-notched samples, while for both V- and U-notches three notch tip radii of ρ= 1, 2, and 4 mm are taken into account. Four mixed-mode I/II loading angles of β = {0°, 10°, 20°, mode II} and three repetitions for each notch opening angle and composite lay-up configuration lead to an overall of 432 fracture tests in the experimental section of the paper, which can provide a good amount of experimental data set for other researchers. Subsequently, in the analytical section, two stress-based fracture criteria accompanied by the virtual isotropic material concept (VIMC) are employed to estimate the fracture loads theoretically. It is demonstrated that using the VIMC approach can yield accurate predictions, while it has much less computational costs compared to the traditional approaches in the literature.

In-situ optical approach to predict mixed mode fracture in a polymeric biomaterial

The present article promotes the usage of the digital image correlation (DIC) technique to determine the in‑situ stress and predict the onset of fracture in a cracked dental biomaterial sample. For this purpose, the elastic and fracture properties of the dental material are measured via the DIC method. To perform mixed mode fracture experiments, a modified single edge notched bend (SENB) specimen with varying crack length is introduced and utilised. From the theoretical point of view, we next implement a stress-based fracture criterion and combine it with two different critical distance models. In this regard, the in‑situ stress is formulated using the data from the DIC analysis conjugated with a supervised learning algorithm. Finally, the crack growth angle and fracture load for the tested biomaterial specimens are estimated, the comparison of which with the experimental measurements reveals good correlation.

A clean cut

The effectiveness of slicing in cutting soft solids (i.e., transverse motion along the blade) is natural to anyone with even the slightest kitchen experience, but the underlying mechanism remains intriguing. This study seeks to unveil the mystic role of slicing by looking into the effect of friction in cutting soft materials. With the increase of indentation depth, the nonlinearity of the large deformation in the superficial layer diverts the lateral stress from the compression of the classic linear elastic solution and introduces a tension that accounts for the ultimate fracture. However, when friction is present between the blade and material, there is always a finite no-slip region on the contact surface, under which stress remains compressive in all directions. The slicing motion of the blade, on the other hand, directs the friction toward the horizontal direction, thus minimizing its contribution in resisting the cutting process in the vertical plane, and enabling a clean cut. Through a numerical model of frictional contact between a cutting wire and a hyperelastic solid, we show that the slicing action diverts the friction force, enables sliding, and facilitates the development of local tension. Without a trustworthy stress-based fracture criterion for soft solids, we then study the energetics of the cutting process. By introducing a small pre-existing crack underneath the blade, we compute the energy landscape of the system and show that the friction reduction in the vertical plane greatly decreases the energy barrier of crack opening and thus promotes cutting.

Effect of pedicle screw angles on the fracture risk of the human vertebra: A patient-specific computational model

The assessment of a human vertebra’s stability after a screws fixation procedure and its fracture risk is still an open clinical problem. The accurate evaluation of fracture risk requires that all fracture mechanical determinants such as geometry, constitutive behavior, loading modes, and screws angulation are accounted for, which requires biomechanics-based analyses. As such, in the present work we investigate the effect of pedicle screws angulation on a patient-specific model of non osteoporotic lumbar vertebra, derived from clinical CT images. We propose a novel computational approach of fracture analysis and compare the effects of fixation stability in the lumbar spine. We considered a CT-based three-dimensional FE model of bilaterally instrumented L4 vertebra virtually implanting pedicle screws according to clinical guidelines. Nine screws trajectories were selected combining three craniocaudal and mediolateral angles, thus investigated through a parametric computational analysis. Bone was modeled as an elastic material with element-wise inhomogeneous properties fine-tuned on CT data. We implemented a custom algorithm to identify the thin cortical layer correctly from CT images ensuring reliable material properties in the computational model. Physiological motion (i.e., flexion, extension, axial rotation, lateral bending) was further accomplished by simultaneously loading the vertebra and the implant. We simulated local progressive damage of the bone by using a quasi-static force-driven incremental approach and considering a stress-based fracture criterion. Ductile-like and brittle-like fractures were found. Statistical analyses show significant differences comparing screws trajectories and averaging the results among six loading modes. In particular, we identified the caudomedial trajectory as the least critical case, thus safer from a clinical perspective. Instead, medial and craniolaterally oriented screws entailed higher peak and average stresses, though no statistical evidence classified such loads as the most critical scenarios. A quantitative validation procedure will be required in the future to translate our findings into clinical practice. Besides, to apply the results to the target osteoporotic population, new studies will be needed, including a specimen from an osteoporotic patient and the effect of osteoporosis on the constitutive model of bone.

An octahedral stress-based fracture criterion for hyperelastic materials

No unified stress-based criterion exists, in the literature, for predicting the rupture of hyperelastic materials subjected to mutiaxial loading paths. This paper aims to establish a generalized rupture criterion under plane stress loading for elastomers. First, the experimental set up, at breaking, including various loading modes, is briefly described and commented. It consists of uniaxial tests, biaxial tests and pure shear tests, performed on different rubbers. The used vulcanizate and thermoplastic rubber materials are a Natural Rubber (NR), a Styrene Butadiene Rubber (SBR), a Polyurethane (PU) and a Thermoplastic elastomer (TPE). Then, we have investigated a new theoretical approach, based upon the principal stresses, to establish a failure criterion under quasi-static loadings. Thus, we have proposed a new analytical model expressed as a function of octahedral stresses. Quite good agreement is highlighted when comparing the ultimate stresses, at break, between the experimental data and the prediction of the proposed criteria using our rubber-like materials.

Experimental verification of the virtual isotropic material concept for the last-ply-failure of U-notched quasi-isotropic E-glass/epoxy composite laminates under tension-shear loading

Fracture investigation of U-notched E-glass/epoxy laminated composite specimens with various notch root radii is performed under mixed mode I/II loading conditions both experimentally and theoretically. Rectangular E-glass/epoxy composite laminates with two numbers of ply (8-ply and 16-ply) and the quasi-isotropic [0/90/+45/–45]s lay-up configuration are fabricated for conducting the fracture tests. To measure the damage initiation angles (DIAs) and the last-ply-failure (LPF) loads of the fabricated composite samples containing horizontal and inclined U-notches, as the main aim of this study, the specimens are loaded under tension by the universal testing machine. The experimental LPF loads are theoretically predicted with the aid of a novel concept, called the Virtual Isotropic Material Concept (VIMC). The proposed VIMC is linked to the two well-known stress-based fracture criteria, namely the maximum tangential stress (MTS) and the mean stress (MS) criteria, in the context of the linear elastic notch fracture mechanics (LENFM). It is proved that the two combined criteria, namely the VIMC-MTS and VIMC-MS criteria, can predict well the LPF loads of the U-notched laminated composite specimens tested under mixed mode I/II loading conditions. One of the important merits of these new criteria is that the predictions of the LPF loads of the U-notched composite specimens are performed without complicated and time-wasting ply-by-ply damage analyses.

Experimental and stress-based theoretical studies on mixed mode I/III fracture of round-tip V-notched Polystyrene specimens

A series of fracture experiments are carried out on the round-tip V-notched GPPS (general-purpose Polystyrene) specimens under various combinations of tension and out-of-plane shear (mixed mode I/III loadings). The test samples are prepared with three different notch opening angles of 30°, 60°, and 90° and four different notch tip radii of 0.5, 1, 2, and 4 mm. Two stress-based fracture criteria entitled mean stress (MS) and point stress (PS) are employed to predict the fracture resistance and fracture initiation angle of the V-notched rectangular specimens. An acceptable consistency is observed between the theoretical predictions and the experimental values of the fracture resistance and fracture initiation angle attained for all the considered notch tip radii and notch opening angles. No meaningful preference is found between the two criteria from the aspect of accuracy of predicting the brittle fracture of V-notched GPPS components. It is also shown that the out-of-plane fracture initiation angles due to mixed mode I/III loading cases are slightly larger for the V-notched members with smaller notch tip radii.

Modelling and characterisation of the high-rate behaviour of rock material

For future reliable numerical simulations of impact wear on steel structures caused by rock material, knowledge about the dynamic mechanical properties of rock material is required. This paper describes the experimental and numerical work to investigate the dynamic mechanical properties of diabase (dolerite), a subvolcanic rock material. In this study, diabase from southern Sweden was used. The impact compressive strength of diabase with a density of 2.63 g/cm3 was examined by using the split-Hopkinson pressure bar (Kolsky bar) method. Cylindrical specimens were used, with a diameter of 8.9 mm and a length of 14 mm. To characterise the rock material, uniaxial compression tests were performed, at high strain rates (150 s-1). Using an inverse modelling approach, material parameters for an elastic constitutive model, with a stress-based fracture criterion were determined. The constitutive model was used in a finite element simulation of a high strain rate uniaxial compression test. Results obtained from the numerical model were in line with the experimental results.

Crack path stability in brittle fracture under pure mode I loading

The crack growth path is expected to be along the initial crack line when the pre-cracked components possess symmetric geometry and loading conditions relative to the crack line. However, it has been previously shown that in some mode I specimens the path of crack growth is not stable and deviates from its initial line after some stages of crack growth. The aim of this paper is to develop an energy-based theoretical model for predicting the instability in the path of crack growth. The theoretical model takes into account both the singular term of stress ahead of the crack tip and the first non-singular term known as the T-stress. The corresponding two-term stresses are replaced in the energy relation around the crack tip and a model is extracted for predicting instability of crack path under mode I loading. The results obtained from the energy-based criterion was then compared to the results obtained from the well-known Generalized Maximum Tangential Stress (GMTS) criterion, which is a two-parameter stress-based fracture criterion that considers the effect of T-stress. To validate the theoretical model, the experimental results published recently from fracture test on several mode I cracked specimens are used. Very good prediction is provided for the path of crack growth in these specimens. It is shown the crack path instability is significantly geometry dependent and can be prevented by modifying the specimen geometry or loading type. The results obtained in this research are important because an appropriate knowledge about the stability of crack path and fracture trajectory can play a key role on the extent of damage that occurs in a cracked structure when it experiences mode I brittle fracture.

A stress-based fracture criteria validated on mixed microstructures of ferrite and bainite over a range of stress triaxialities

Hot stamping is a sequential process for formation and heat-treatment of sheet metal components with superior mechanical properties. By applying different cooling rates, the microstructural composition and thus the material properties of steel can be designed. By controlling the cooling rate in different sections of a blank, the material properties can be tailored depending on the desired toughness. Under continuous cooling, various volume fractions of ferrite and bainite are formed depending on the rate of cooling. This paper focuses on the ductile fracture behavior of a thin sheet metal made of low-alloyed boron steel with varying amounts of ferrite and bainite. An experimental setup was applied in order to produce microstructures with different volume fractions of ferrite and bainite. In total, five different test specimen geometries, representing different stress triaxialities, were heat treated and tensile tested. Through full-field measurements, flow curves extending beyond necking and the equivalent plastic strain to fracture were determined. Experimental results were further investigated using a mean-field homogenization scheme combined with local fracture criteria. The mean-field homogenization scheme comprises the influence of microstructure composition and stress triaxiality with usable accuracy, connoting auspicious possibilities for constitutive modeling of hot-stamped components.

Strain-based criteria for mixed-mode fracture of polycrystalline graphite

The mixed-mode brittle fracture of two types of commercial graphite is investigated focusing on strain-based fracture criteria. The previously published experiments using centrally-cracked Brazilian disk specimens subjected to mixed-mode loadings are simulated by two strain-based fracture criteria: the traditional maximum tangential strain (MTSN) criterion only considering the singular terms, and the extended maximum tangential strain (EMTSN) criterion, which considers the first nonsingular strain term as well as the singular terms. Numerical simulations on the centrally-cracked Brazilian disk specimen show that the first nonsingular tangential strain term significantly influences the tangential strain distribution around the crack tip. The comparison of the evaluations by the MTSN and EMTSN criteria with the experimental data shows that the EMTSN criterion is more capable of successfully estimating the fracture resistance of graphite materials rather than the traditional MTSN criterion. In addition, when the first nonsingular term is considered, the strain-based fracture criterion provides better predictions for near mode II loadings than the stress-based fracture criterion.

Numerical failure analysis of steel sheets using a localization enhanced element and a stress based fracture criterion

Strain localization and fracture initiation of elasto-plastic thin steel sheets is analyzed. A shell element enhanced by embedded discontinuities is developed to improve coarse-mesh accuracy in terms of fracture initiation prediction and to regularize the post-instability response. Discontinuities in the strain field are introduced when instability is signaled by a local bifurcation analysis. The enhancements are implemented for the Belytschko–Lin–Tsay shell element. This is combined with a stress based fracture criterion which relates the magnitude of the stress vector and the first invariant of the stress tensor. A robust experimental procedure based on full-field measurements enable direct calibration in stress space, and provides a flow curve up to large strains. Numerical examples involving tensile samples with different localization behavior are presented to demonstrate significant reduction of spurious mesh dependence. Moreover, the engineering feasibility of the direct use of a stress based fracture criterion in combination with the enhanced element is evaluated by comparison of measured and calculated fracture elongations.

Impact Fracture of Jointed Steel Plates of Bolted Joint of Cars

The present study is concerned with the development of a fracture criterion for the impact fracture of jointed steel plates of a lap bolted joint used in the suspension parts of a car body. For the accurate prediction of crash characteristics of car bodies by computer-aided engineering (CAE), it is also necessary to examine the behaviour and fracture of the jointed steel plates subjected to impact loads. Although the actual impact fracture of jointed steel plates of a lap bolted joint in cars is complicated, for simplifying it is classified into the shear fracture and the extractive fracture of jointed steel plates. Three kinds of steel plates, i.e., common steel with the tensile strength of 270 MPa and two high tensile strength steels with the tensile strength of 440 and 590 MPa level used for vehicles, are examined. In the impact shear test, the specimens are made of two plates and jointed by a bolt, and in the impact extractive test the specimens are made of a plate and drilled in the centre for a bolt. The impact shear test of jointed steel plates of lap bolted joints is performed using a modified split Hopkinson bar apparatus, while the impact extractive one is performed using one-bar method. Numerical simulations by a FEM code LS-DYNA are also carried out in order to understand the mechanism of shearing and extractive fractures process of jointed steel plates. The obtained results suggest that a stress-based fracture criterion may be developed for the impact shearing and extractive fractures of jointed steel plates of lap bolted joints used in a car body.

Numerical and Experimental Determination of Cut-edge after Blanking of Thin Steel Sheet of DP1000 within Use of Stress based Damage Model

The proposed study focuses on blanking of thin steel sheets of Dogal1000DP +Z100MBO. Numerical and experimental investigations of the influence of clearance and punch speed on the cutting force and the geometry of the sheared edge were done. Tensile and stack compression test at elevated temperatures has been chosen to determine the flow and fracture behavior of Dogal1000DP +Z100MBO at different stress states. It is shown that the flow curve determined by stack compression test leads to better results in force - displacement prediction of a blanking process compared to determination of flow curve by tensile test. Stress based fracture criterion were chosen to describe damage behaviour. Moreover significant influence of fracture locus for negative stress triaxialities on the geometry of the numerically predicted sheared edge is shown.

Shear fracture of jointed steel plates of bolted joints under impact load

The present study is concerned with the development of a fracture criterion for the impact fracture of jointed steel plates of bolted joints used in a car body, which contributes to crash simulations by CAE. We focus our attention on the shear fracture of the jointed steel plates of lap-bolted joints in the suspension of a car under impact load. Members of lap-bolted joints are modelled as a pair of steel plates connected by a bolt. One of the plates is a specimen subjected to plastic deformation and fracture and the other is a jig subjected to elastic deformation only. Three kinds of steel plate specimens are examined, i.e., a common steel plate with a tensile strength of 270 MPa and high tensile strength steel plates of 440 and 590 MPa used for cars. The impact shear test was performed using the split Hopkinson bar technique for tension impact, together with the static test using a universal testing machine INSTRON 5586. The behaviour of the shear stress and deformation up to rupture taking place in the joint was discussed. The obtained results suggest that a stress-based fracture criterion may be developed for the impact fracture of jointed steel plates of a lap-bolted joint.

Characterization modelling and validation of a two-point loaded iron ore pellet

Iron ore pellets are sintered, centimetre-sized spheres of ore with high iron content. Together with carbonized coal, iron ore pellets are used in the production of steel. In the transportation from the pelletizing plants to the customers, the iron ore pellets are exposed to different stresses, resulting in degradation of strength and in some cases fragmentation. For future reliable numerical simulations of the handling and transportation of iron ore pellets, knowledge about their mechanical properties is needed. This paper describes the experimental and numerical work to investigate the mechanical properties of blast furnace iron ore pellets. To study the load deformation behavior and the fracture of iron ore pellets, a number of point load tests are carried out and analyzed. Material parameters for an elastic–plastic constitutive model with linear hardening for iron ore pellets are derived and expressed in terms of statistical means and standard deviations. Two finite element models are developed for different purposes. For the material parameter determination, a perfectly spherical model is used. The constitutive model is validated with a finite element model based on a representative optically scanned iron ore pellet. The proposed constitutive model is capturing the force displacement relation for iron ore pellets in a two-point load test. A stress based fracture criterion which takes the triaxiality into account is suggested and calculated as the maximum equivalent effective stress dependent on the three principal stresses at fracture. The results of this study show that the equivalent effective stress in the vicinity of the centre of an irregular model of an iron ore pellet is very close to the results of a model of a perfectly spherical iron ore pellet. The proposed fracture criterion indicates fracture in the representative iron ore pellet model coincident with the location of the crack developed during the test of the optically scanned iron ore pellet.

Impact extractive fracture of jointed steel plates of a bolted joint

This study is concerned with the development of a fracture criterion for the impact fracture of jointed steel plates of a bolted joint used in a car body. For the accurate prediction of crash characteristics of car bodies by computer-aided engineering (CAE), it is also necessary to examine the behavior and fracture of jointed steel plates subjected to impact loads. Although the actual impact fracture of jointed steel plates of a bolted joint used in cars is complicated, for simplifying the problem it might be classified into the shear fracture and the extractive fracture of jointed steel plates. Attention is given to the extractive fracture of jointed steel plates in this study. The extractive behavior and fracture of three kinds of steel plates used for cars are examined in experiments and numerical simulations. The impact extraction test of steel plates jointed by a bolt is performed using the one-bar method, together with the static test. In order to understand the mechanism of extractive fracture process of jointed steel plates, numerical simulations by a FEM code LS-DYNA are also carried out. The obtained results suggest that a stress-based fracture criterion may be developed for the impact extractive fracture of jointed steel plates of a bolted joint used in a car body.

Impact Pull-Out Fracture of Steel Plates Jointed by Bolt

Collision safety and reliability of cars under impact loading become more and more important in the vehicle industries. This study is concerned with the development of a fracture criterion for the impact fracture of jointed steel plates of a bolted joint used in a car body, which may contribute to crash simulations by computer-aided engineering (CAE). The impact behavior and fracture of jointed steel plates of a bolted joint were examined by experiments and numerical simulations. The impact pull-out test of jointed steel plates by a bolt was performed by making use of an one-bar method for impact tests, together with the static test using a universal testing machine INSTRON 5586. In order to understand the mechanism of fracture process of the jointed steel plate, numerical simulations by FEM code ANSYS and LS-DYNA were also carried out. The rupture of steel plates jointed by a bolt with washers occurred along the circular outside of washers and made a hole with the same diameter as washers for both of static and impact loading conditions, and then the pull-out load (F) increased with increasing of the diameter of washers. On introducing the pull-out stress defined as (F/A) for convenience, in which A is the cross-sectional area of the steel plate along the circumference of a washer, the pull-out strength showed almost the same value regardless of the washer size. This result suggests that a stress-based fracture criterion may be developed for the impact fracture of jointed steel plates of bolted joint used in a car body.