A comparative study of dynamic, ductile fracture initiation in two specimen configurations

In this work a single edge notched plate (SEN(T)) subjected to a tensile stress pulse is analysed, using a 2D plane strain dynamic finite element procedure. The interaction of the notch with a pre-nucleated hole ahead of it is examined. The background material is modelled by the Gurson constitutive law and ductile failure by microvoid coalescence in the ligament connecting the notch and the hole is simulated. Both rate independent and rate dependent material behaviour is considered. The notch tip region is subjected to a range of loading rates J by varying the peak value and the rise time of the applied stress pulse. The results obtained from these simulations are compared with a three point bend (TPB) specimen subjected to impact loading analysed in an earlier work [3]. The variation of J at fracture initiation, J _c, with average loading rate J is obtained from the finite element simulations. It is found that the functional relationship between J _c and J is fairly independent of the specimen geometry and is only dependent on material behaviour.     

Dynamic ductile crack growth and transition to cleavage – a cell model approach

The fracture behavior of ferritic steel in the transition regime is controlled by the competition between ductile tearing and cleavage. Many test specimens that failed by catastrophic cleavage showed significant amounts of ductile tearing prior to cleavage fracture. The transition from ductile tearing to cleavage has been attributed to the increase in constraint and sampling volume associated with ductile crack growth. This work examines the role of dynamic ductile crack growth on the fracture mode transition by way of a cell model of the material. The cell model incorporates the effects of stress triaxiality and strain rate on material failure characteristics of hole growth and coalescence. Loading rate and microstructure effects on the stress fields that evolve with rapid (ductile) crack growth are systematically studied. The stress fields are employed to compute the Weibull stress which provides probability estimates for the susceptibility to cleavage fracture. A center-cracked panel subjected to remote tension is the model problem under study. The computational model uses an elastic-viscoplastic constitutive relation which incorporates enhanced strain rate hardening at high strain rates. Adiabatic heating due to plastic dissipation and the resulting thermal softening are also accounted for. Under dynamically high loading rate, our model shows the crack speed achieves its peak value soon after crack initiation and quickly falls off to slower speeds with further crack growth. Remarkably, the Weibull stress follows a similar pattern which suggests that the transition to the cleavage fracture is most likely to occur, if at all, at the peak speed of ductile crack growth. Key words: Dynamic fracture, ductile tearing, crack growth, transition regime, cleavage fracture, cell model, finite element.     

Numerical study of fracture plane control in laboratory-scale blasting

One way of achieving controlled crack growth is to introduce notches into the surface of the guide hole wall. This results in high stress concentration at the notch tips when the stress wave reaches the guide hole. This paper presents the estimated fracture properties for analyzing blasting-induced fracture processes in PMMA specimens. The model experiments, which have a notched guide hole between the charge holes, were simulated using dynamic fracture process analysis (DFPA) software to examine the effect of the notched guide hole on fracture plane control. The influence of the location of the guide hole and the initiation time lag on the crack propagation control is discussed, as is the relationship between the applied fracture energy and crack extension.     

Numerical modelling of fracture initiation in large steel specimens at impact

Dynamic mode I fracture initiation in impact loaded single edge bend specimens with a quarter notch is investigated by numerical modelling and the results are compared with sets of experimental data from two different steel qualities. The finite element analysis include 2D (two-dimensional) plane strain, 2D plane stress and 3D models. No crack growth is included in the calculations. The impact velocities are approximately 15, 30 and 45 m/s and the specimen size is 320×75 mm² with a thickness of 20 or 40 mm. Some specimens have side grooves. Details of the deflection of the specimens are accurately reproduced prior to crack initiation both by the 2D plane strain model and by the 3D model.The experiments were performed in the ductile to brittle transition region. It is assumed that cleavage fracture initiation can be predicted by the Ritchie-Knott-Rice (RKR) model, i.e. cleavage fracture initiates when the opening stress exceeds the macroscopic cleavage stress over a fixed, critical distance. At an impact velocity of 15 m/s, fracture initiation by void nucleation and growth is observed, though the RKR-conditions is seemingly fulfilled according to the computational results. Possible limitations in the use of the RKR model are discussed.     

Numerical simulations of hole growth and ductile fracture initiation under mixed-mode loading

Numerical simulations of ductile fracture initiation caused by the interaction between a notch tip and a nearby hole under mixed-mode loading involving modes I and II are performed. Attention is restricted to plane strain, small-scale yielding conditions. The Gurson constitutive model that accounts for the ductile failure mechanisms of micro-void nucleation, growth and coalescence is employed within the framework of a finite deformation plasticity theory. The failure of the ligament connecting the notch tip and the hole by either microvoid coalescence or by intense plastic strain localization is modelled. The effect of mode-mixity on the notch tip deformation, hole growth and the critical value of J at fracture initiation is examined. The dominant failure mechanism which is operative near the notch tip for various extents of mixity of modes I and II is identified.     

Experimental studies on mixed‐mode dynamic fracture behaviour of aluminium alloy plates with narrow U‐notch

Mixed‐mode dynamic fracture behaviour of cast aluminium alloy ZL205A thin plates with narrow U‐notch was studied by split Hopkinson tensile bar apparatus. Specimens with different loading angles were designed to realize different fracture modes. The same loading condition was maintained during the tests. Recovery specimens show that crack propagates along the notch direction. Force–elongation relations show that with the loading angle increasing, the fracture force increases while the final elongation decreases. Deformation and fracture process was observed by a high‐speed camera. Displacement distribution around the crack was calculated through digital image correlation technique. Based on the photos and displacement results, initiation time of the crack was derived. Besides, two stress components (normal stress and shear stress) applied on the fracture surface were investigated. Results show that crack initiation stresses at different loading angles satisfy the ellipse equation. Pure mode I and II fracture stresses are 425.3 and 236.7 MPa, respectively. Furthermore, specific fracture energy of different specimens was calculated. The energy data vary with loading angle and located on an approximate upward parabolic curve. From the curve, the minimum specific fracture energy of the thin plate specimen is 42.0 kJ/m² under loading angle of 76.3°.     

Impact and dynamic fracture of tough polymers by thermal decohesion in a Dugdale zone

At low temperatures and high loading rates, normally tough crystalline thermoplastics may undergo a transition from ductile tearing to brittle rapid crack propagation (RCP). It is proposed here that RCP — characterised by low toughness, high crack speed (>100 m/s) and a macroscopically smooth fracture surface — occurs by self-sustained melting of a layer, one chain length thick, at each cohesive surface of a crack-tip craze, due to adiabatic heating. Initiation of RCP from a rapidly loaded sharp notch, i.e. impact fracture, requires both the formation of this melt layer, and sufficient crack extension force to propagate it. A schematic linear-elastic analysis based on the Dugdale model accounts both for the measured dynamic fracture resistance, and for the variation of impact fracture resistance with impact speed, in two pipe-grade polyethylenes and in a neat and a rubber-toughened polyacetal. It is concluded that crack initiation resistance, unlike dynamic fracture resistance, cannot be defined as a geometry-dependent material property.     

Investigation of crack tunneling in ductile materials

Crack tunneling has been commonly observed in crack growth experiments on specimens made of ductile materials such as steel and aluminum alloys. The objective of this study is to investigate the crack tunneling phenomenon and study the effects of crack tunneling on the distribution of several mechanics parameters controlling ductile fracture. Three-dimensional (3D) elastic-plastic finite element analyses of stable tearing experiments involving tunneling fracture are carried out. Two model problems based on stable tearing experiments are considered. The first model problem involves a plate specimen containing a stationary, single-edge crack with a straight or tunneled crack front, under remote mode I loading. In the numerical analyses, the crack tip opening displacement, the von Mises effective stress, the mean stress, the stress constraint and the effective plastic strain around straight and tunneled crack fronts are obtained and compared. It is found that crack tunneling produces significant changes in the stress and deformation fields around the crack front. The second model problem involves a specimen containing a stably growing single-edge crack with a straight or tunneled crack front, under remote mode I loading. Crack growth events with a straight or tunneled crack front are simulated using the finite element method, and the effect of crack tunneling on the prediction of the load-crack-extension response based on a CTOD fracture criterion is investigated.     

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

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

Dynamic crack initiation toughness of 4340 steel at constant loading rates

Determination of fracture toughness for metals under quasi-static loading conditions can follow well-established procedures and ASTM standards. The use of metallic materials in impact related applications requires the determination of dynamic crack initiation toughness for these materials. There are two main challenges in experiment design that must be overcome before valid dynamic data can be obtained. Dynamic equilibrium over the entire specimen needs to be approximately achieved to relate the crack tip loading state to the far-field loading conditions, and the loading rate at the crack tip should be maintained near constant during an experiment to delineate rate effects on the values of dynamic crack initiation toughness. A recently developed experimental technique for determining dynamic crack initiation toughness of brittle materials has been adapted to measure the dynamic crack initiation toughness of high-strength steel alloys. A Kolsky pressure bar is used to apply the dynamic loading. A pulse shaper is used to achieve constant loading rate at the crack tip and dynamic equilibrium across the specimen. A four-point bending configuration is used at the gage section of the setup. Results are presented which show a monotonically increasing rate dependence of crack initiation toughness for 4340 high-strength steel.     

Dynamic fracture mechanics—A scientific tool for the prevention of catastrophic failure

The major area of research in dynamic fracture has been the extension of the concept of static fracture toughness to predict crack arrest for a propagating crack. In this work crack propagation due to a ductile (microvoid) mechanism and cleavage (brittle) mechanism, as well as transition from one mode to another, has been analysed theoretically. Dynamic fracture toughness as a function of crack velocity has been determined. Temperature distribution near a propagating crack tip has been predicted for plane stress condition. The effect of reflected stress wave in a single edge notch specimen under transient crack growth conditions has also been analysed.     

Fracture mechanisms of aluminium alloy AA7075-T651 under various loading conditions

The fracture behaviour of the aluminium alloy AA7075-T651 is investigated for quasi-static and dynamic loading conditions and different stress states. The fracture surfaces obtained in tensile tests on smooth and notched axisymmetric specimens and compression tests on cylindrical specimens are compared to the fracture surfaces that occur when a projectile, having either a blunt or an ogival nose shape, strikes a 20 mm thick plate of the aluminium alloy. The stress state in the impact tests is much more complex and the strain rate significantly higher than in the tensile and compression tests. Optical and scanning electron microscopes are used in the investigation. The fracture surface obtained in tests with smooth axisymmetric specimens indicates that the crack growth is partly intergranular along the grain boundaries or precipitation free zones and partly transgranular by void formation around fine and coarse intermetallic particles. When the stress triaxiality is increased through the introduction of a notch in the tensile specimen, delamination along the grain boundaries in the rolling plane is observed perpendicular to the primary crack. In through-thickness compression tests, the crack propagates within an intense shear band that has orientation about 45° with respect to the load axis. The primary failure modes of the target plate during impact were adiabatic shear banding when struck by a blunt projectile and ductile hole-enlargement when struck by an ogival projectile. Delamination and fragmentation of the plates occurred for both loading cases, but was stronger for the ogival projectile. The delamination in the rolling plane was attributed to intergranular fracture caused by tensile stresses occurring during the penetration event.     

Effect of strength mis-match and dynamic loading on ductile fracture initiation

It has been well known that ductile fracture of steels is accelerated by triaxial stresses. The characteristics of ductile crack initiation in steels are evaluated quantitatively using a two-parameter criterion based on equivalent plastic strain and stress triaxiality.The present study focuses on the effects of geometrical discontinuity, strength mis-match, which can elevate plastic constraint due to heterogeneous plastic straining, and loading rate on the critical condition for ductile fracture initiation using a two-parameter criterion. Fracture initiation testing has been conducted under static and dynamic loading using circumferentially notched round-bar specimens. In order to evaluate the stress/strain state in the specimens, especially under dynamic loading, a thermal elastic-plastic dynamic finite element (FE) analysis considering the temperature rise due to plastic deformation has been carried out.The tensile tests on specimens with an undermatching interlayer showed that the relationship between the critical equivalent plastic strain to initiate ductile fracture and stress triaxiality was equivalent to that obtained on homogeneous specimens under static loading. Moreover, the two-parameter criterion for ductile fracture initiation is shown to be independent of the loading rate. It was demonstrated that the critical global strain to initiate ductile fracture in specimens with strength mis-match under various loading rate can be estimated based on the local criterion, that is two-parameter criterion obtained on homogeneous specimens under static tension, by mean of FE-analysis taken into account accurately both strength mis-match and dynamic loading effects on stress/strain behaviors.     

Dynamic crack propagation in large steel specimens

Dynamic fracture experiments on crack initiation and crack growth in single edge bend specimens are performed. The impact velocity is in the range of 14 to 50 m/s and the specimen size is 320×75 mm with a thickness varying from 18 to 40 mm. The experiments are recorded by high speed photography.Two different steel qualities are investigated and their constitutive characterisation are obtained from uni-axial tension tests and shear tests with strain rates in the range 10⁻⁴ to 10³ s⁻¹ and tension tests at temperatures between −196 and 600°C.One of the materials exhibits a transition from a ductile dimple fracture to a brittle cleavage fracture as the loading velocity increases and as the specimen thickness increases. Scanning electron microscope fractographs show that the density of plastic bridges within cleavage ligaments decreases with increasing impact velocity and with increasing specimen thickness. It is also noted that the local crack propagation direction deflects from the global one in cleavage fracture areas with a high density of plastic bridges.The other material fails in a ductile mode in all the investigated cases.     

Initiation, propagation and arrest of an interface crack subjected to controlled stress wave loading

An experimental study has been conducted to investigate the initiation, propagation, and arrest of bimaterial interface cracks subjected to controlled stress wave loading in the form of a tensile dilatational stress wave pulse. The tensile pulse is generated by detonating lead azide explosive in a specially designed specimen. Dynamic loading of the bimaterial interface results in crack initiation, propagation, and arrest, all in the same experiment. This failure event is observed using photoelasticity in conjunction with high speed photography. Full field data from the experimentally obtained isochromatic fringe patterns is analyzed to determine time histories of various fracture parameters such as the crack tip speed, the dynamic complex stress intensity factor, the energy release rate, and the mixity. The experimental data is also used to quantify the values of the dynamic initiation and arrest toughness and to evaluate a recently proposed dynamic interface fracture criterion. This revised version was published online in August 2006 with corrections to the Cover Date.     

Quasi-static and dynamic fracture behaviour of rock materials: phenomena and mechanisms

An experimental investigation is conducted to study the quasi-static and dynamic fracture behaviour of sedimentary, igneous and metamorphic rocks. The notched semi-circular bending method has been employed to determine fracture parameters over a wide range of loading rates using both a servo-hydraulic machine and a split Hopkinson pressure bar. The time to fracture, crack speed and velocity of the flying fragment are measured by strain gauges, crack propagation gauge and high-speed photography on the macroscopic level. Dynamic crack initiation toughness is determined from the dynamic stress intensity factor at the time to fracture, and dynamic crack growth toughness is derived by the dynamic fracture energy at a specific crack speed. Systematic fractographic studies on fracture surface are carried out to examine the micromechanisms of fracture. This study reveals clearly that: (1) the crack initiation and growth toughness increase with increasing loading rate and crack speed; (2) the kinetic energy of the flying fragments increases with increasing striking speed; (3) the dynamic fracture energy increases rapidly with the increase of crack speed, and a semi-empirical rate-dependent model is proposed; and (4) the characteristics of fracture surface imply that the failure mechanisms depend on loading rate and rock microstructure.     

基于键基近场动力学理论的单裂纹圆孔板冲击破坏研究

基于键基近场动力学理论,建立分离式霍普金森杆冲击单裂纹圆孔板动力学模型,其中霍普金森杆用一维PD模型、单裂纹圆孔板用二维PD模型描述,采用短程斥力模型描述碰撞过程,模拟冲击压缩条件下单裂纹圆孔板动态破坏行为。通过试样端面受力分析得到端面载荷的V形分布规律,解决了传统实验-数值研究法在端面加载上的局限性。研究不同入射速度下试件裂纹的扩展过程和破坏模式,准确捕获了裂纹起裂、止裂及二次起裂时间。根据键基近场动力学理论下材料动态应力强度因子计算方法,求得裂纹的起裂韧度,为材料动态断裂韧度计算提供了新的途径。     

Fatigue voids and their significance

ABSTRACT Fractures from tests on 2014‐T6511 and 2024‐T3 test coupons under specially designed programmed loading reveal voids with distinct fatigue markings. These ‘fatigue voids’ appear to form as a consequence of the separation of noncoherent secondary particulates from the matrix in early fatigue. The process of their formation is through the initiation, growth and coalescence of multiple interfacial cracks around the particulate. Such voids become visible on the fatigue fracture surface if and when the crack front advances through them. In vacuum, each fatigue void is the potential initiator of an embedded penny‐shaped crack. The one closest to the specimen surface is likely to become the dominant crack, indicating that fatigue voids appear to be the likely origins of the dominant crack in vacuum. In air, the dominant crack forms at the notch surface and grows much faster, giving less opportunity for multiple internal cracks to spawn off from the innumerable internal fatigue‐voids. Thus in air, fatigue voids do not appear to affect the fatigue process at low and intermediate growth rates. At high crack growth rates involving considerable crack tip shear, slip planes with particulate concentration offer the path of least resistance. This explains the increasing density of fatigue voids with growth rate. Very high growth rates signal the onset of a quasi‐static crack growth component that manifests itself through growing clusters of microvoid coalescence associated with static fracture. Fatigue voids are likely to form in other Al‐alloys with secondary noncoherent particulates. They have nothing in common with microvoids associated with ductile fracture.