Crack straining-based spall model

Mean void growth-based spall models that avoid the complications of nucleation have been successfully applied to the problem of ductile spallation. However, similar models based on mean crack growth, applicable to brittle spallation, are not promising. This is because it remains to be demonstrated how an appropriate mean crack size is chosen to identify the brittle spall strength as the threshold pressure for crack growth. In the authors' view, the solidity evolution is not merely a consequence of the nucleation and growth of cracks but also determined by the crack straining caused by the relaxed tensile pressure. This paper presents a crack straining-based spall model which assumes that the inelastic volumetric strain caused by the relaxed tensile pressure at a critical fragment volume is the main factor governing the solidity evolution during the process of coalescence and fragmentation. Such an approach makes the modelling of brittle spall compatible with that of ductile. The developed model requires only two additional parameters to those required by the chosen constitutive model and equation of state. We present the comparisons between experimental and computational simulation of the free surface velocity history of the target in a plane impact plate experiment. These show very good agreement.     

Copper spall fracture under sub-nanosecond electron irradiation

Ultra-short powerful electron beam is a suitable tool for producing of high rate deformation in substance. In paper we present a new model of high rate fracture and use this model for numerical investigation of fracture of copper target at irradiation by sub-nanosecond electron beam. In this model, fracture is considered as a time-dependent process of nucleation and growth of opening mode cracks. The nucleation and growth rates are controlled by specific free energy of crack surface which is sole fitted parameter. Plastic deformations, both in cracks vicinity and total in substance, are described in frames of dislocation theory. For verification of the model, we performed simulations of spall fracture at plate impact and at irradiation by high-current electron beam with pulse duration of tens of nanoseconds, and reasonable agreement with experimental data has been demonstrated. Simulations of the sub-nanosecond electron beam action on target indicate that spall fracture of the irradiated target surface is possible. This fracture takes place at the enclosed energy density slightly below the value, which is sufficient for melting of irradiated substance. Fracture threshold energy density does not depend on the origin dislocation density and it increases with the increase of pulse duration. As a result, at long pulse durations (more than ten nanoseconds) the substance melts before fracture.     

Effect of Grain Size on the Spall Fracture Behaviour of Pure Copper under Plate‐Impact Loading

The effects of grain size on the spall response were investigated for high purity copper materials by plate‐impact experiments including real‐time measurements of the free surface velocity profiles as well as post‐impact fractography studies on the soft‐recovered samples. High purity copper plates were cold rolled and heat treated to produce recrystallized samples with average grain sizes of 78, 273 and 400 μm, respectively. The spall strength estimated from the free surface velocity profile is nearly constant with no significant effect on the grain size. However, differences are observed in the acceleration rate of velocity rebound beyond the minima. This may be attributed to the effect of grain size on the growth rate of damage. Metallographic analyses of the fracture surface show that the characteristic feature of the fracture surface clearly depends on the grain size. In the 78‐ and 273‐μm samples, the fracture surfaces are decorated with large, high‐density ductile dimples suggesting that the preferential failure mode is ductile intergranular fracture. In the 400‐μm samples, the fracture surfaces have a rock candy appearance with small, high density brittle dimples as well as large ductile dimples suggesting that the fracture mode is a mix of both brittle intergranular fracture and ductile transgranular fracture.     

Wedge crack nucleation in Type 316 stainless steel

Type 316 austenitic steel has been heat-treated to produce a range of grain sizes and then creep-tested at 625° C at various stresses so as to examine the nucleation and the factors which effect the nucleation of grain-boundary triple point or wedge cracks. An internal marker technique was used to evaluate the extent of the grain-boundary sliding in relation to the total creep strain. Triple point crack nucleation occurred over the entire range of grain sizes and stresses examined when the product of the stress and grain-boundary displacement reached a critical value; the effective surface energy for grain boundary fracture, estimated using an expression derived by Stroh, was in approximate agreement with the surface free energy value indicating that only limited relaxation occurred by plastic deformation. The first cracks were observed to form along grain boundary facets perpendicular to the applied stress direction and with the sliding grain boundaries at high angles (60 to 80°) to the crack growth direction. Subsequent cracking occurred under conditions which deviated slightly from this initial condition, and the increase in crack density with strain was expressed in terms of geometrical factors which take account of the orientation effects.     

A FINITE ELEMENT TECHNIQUE TO SIMULATE THE STABLE SHAPE EVOLUTION OF PLANAR CRACKS WITH AN APPLICATION TO A SEMI-ELLIPTICAL SURFACE CRACK IN A BIMATERIAL FINITE SOLID

This paper describes a numerical procedure to model the crack front evolution of initially arbitrary shaped planar cracks in a three-dimensional solid. The influence of a bimaterial interface on the fracture path of a semi-elliptical surface crack in a three-dimensional structure is examined. The analysis is based on the assumption that fracture is controlled by small-scale yielding and linear elastic fracture mechanics. The finite element method and the crack-tip contour J-integral in a volume domain representation are utilized to calculate the crack front energy release rate. The computed values of the energy release rate are used with a crack-tip velocity growth law to model crack growth increment. The progress of the crack growth evolution is brought forward by successive iterations. Examples of computed crack evolution are given for an embedded circular crack, a semi-elliptical surface crack in a finite plate, and a configuration that defines an isotropic homogeneous material layer with a surface crack located between two material layers. © 1997 by John Wiley & Sons, Ltd.     

DJ4热卷弹簧纵向裂纹的原因分析和解决措施

采用表面形态、金相组织、硬度和冲击断口分析等方法对淬火纵向开裂DJ4弹簧进行了分析。结果表明，制扁后表面缺陷、脱碳及夹杂物的纵向分布，是产生纵向裂纹的诱因；卷制前加热温度过高，晶粒粗大，是产生纵向裂纹的主要原因。提出了整改措施，即对热处理工艺的调整和卷制后空冷到600℃重结晶细化晶粒，抑制了纵向裂纹的产生，使冲击断裂韧性得到较大提高。     

Microstructural modelling of creep crack growth from a blunted crack

The effect of crack tip blunting on the initial stages of creep crack growth is investigated by means of a planar microstructural model in which grains are represented discretely. The actual linking-up process of discrete microcracks with the macroscopic crack is simulated, with full account of the underlying physical mechanisms such as the nucleation, growth and coalescence of grain boundary cavities accompanied by grain boundary sliding. Results are presented for -controlled mode I crack growth under small-scale damage conditions. Particular attention is focused on creep constrained vs. unconstrained growth. Also the effect of grain boundary shear stresses on linking-up is investigated through shear-modified nucleation and growth models. The computations show a general trend that while an initially sharp crack tends to propagate away from the original crack plane, crack tip blunting reduces the crack growth direction. Under unconstrained conditions this can be partly rationalized by the strain rate and facet stress distribution corresponding to steady-state creep. This revised version was published online in August 2006 with corrections to the Cover Date.     

Microscale characterization of granular deformation near a crack tip

This paper presents a study of microscale plastic deformation at the crack tip and the effect of microstructure feature on the local deformation of aluminum specimen during fracture test. Three-point bending test of aluminum specimen was conducted inside a scanning electron microscopy (SEM) imaging system. The crack tip deformation was measured in situ utilizing SEM imaging capabilities and the digital image correlation (DIC) full-field deformation measurement technique. The microstructure feature at the crack tip was examined to understand its effect on the local deformation fields. Microscale pattern that was suitable for the DIC technique was generated on the specimen surface using sputter coating through a copper mesh before the fracture test. A series of SEM images of the specimen surface were acquired using in situ backscattered electronic imaging (BEI) mode during the test. The DIC technique was then applied to these SEM images to calculate the full-field deformation around the crack tip. The grain orientation map at the same location was obtained from electron backscattered diffraction (EBSD), which was superimposed on a DIC strain map to study the relationship between the microstructure feature and the evolution of plastic deformation at the crack tip. This approach enables to track the initiation and evolution of plastic deformation in grains adjacent to the crack tip. Furthermore, bifurcation of the crack due to intragranular and intergranular crack growth was observed. There was also localization of strain along a grain boundary ahead of and parallel to the crack after the maximum load was reached, which was a characteristic of Dugdale–Barenblatt strip-yield zone. Thus, it appears that there is a mixture of effects in the fracture process zone at the crack tip where the weaker aspects of the grain boundary controls the growth of the crack and the more ductile aspects of the grains themselves dissipate the energy and the corresponding strain level available for these processes through plastic work.     

Slow crack growth in Si3N4 at room temperature

Tests of Si₃N₄ hot pressed with various types and levels of oxide additives show evidence of room temperature slow crack growth in delayed failure tests (using natural flaws), but not in fracture mechanics (e.g. DCB or DT) tests consistent with more limited literature data for these two types of tests. Neither type of test showed slow crack growth in either CVD Si₃N₄ or RSSN. Further the fracture mode in the latter two materials was essentially all transgranular, while it was predominantly (e.g. 80%) intergranular in the hot-pressed materials. It was thus postulated that (1) the oxide grain boundary phase is responsible for slow crack growth and; (2) varying distribution of the oxide boundary phase and grain boundary character result in sufficient boundaries not susceptible to slow crack growth to pin cracks with macroscopic crack lengths (i.e. as in DCB and DT tests). Both the much smaller crack front lengths and the large number of small (natural, e.g. machining) flaws allows some of these small flaws to grow to critical size, thus leading to delayed failure in the hot-pressed materials.     

Cavitation erosion as a kind of dynamic damage

The purpose of this work is to show that the spherical shock waves arising in a liquid during cavitation bubble collapse can lead to formation of deep needle-like pits on the solid surface. The nature of dynamic damage during cavitation erosion is the spallation caused by interference of rarefaction waves. Rarefaction at spherical wave impact arises when the velocity of contact surface boundary becomes less than the speed of sound in a target. If the tension caused by the focused rarefaction wave exceeds the spall strength of material, channel spall cracks can arise. At low pulsed loading, spall cracks are formed in a dynamic fatigue mode. Needle-like damage arises upon focusing rarefaction waves. In terms of our model, a system of cylindrical spall cracks is consecutively formed around a deeper axial spall needle-like crack. Upon subsequent loading, each crack acts as a source of new rarefaction wave. Newly formed cylindrical spall cracks suppress the growth of the cracks of previous generation and give birth to the cracks of next generation. A distinctive feature is that the cracks are first formed at the periphery of damageability zone, subsequent cracks having a lower depth.     

The effects of stress ratio and grain size on near-threshold fatigue crack propagation in low-carbon steel

The effects of the stress ratio and the grain size on the fatigue crack growth near the threshold in a low carbon steel were analysed based on the crack-closure measurement and the microscopic observations of cracktip slip deformation and the fracture surface. The low-rate region A was divided into regions A1 and A2 in the relation of the rate against the effective stress intensity range. In regions A2 and B, the rate was expressed in a unique power function of the effective range without respect to the stress ratio and the grain size. In region A1 very close to the threshold, the rate was slower for larger grain sized material, and the effective threshold stress intensity factor increased linearly with the square root of the grain size. The slip-band zone in this region was rather independent of the stress intensity and was sized by the grain dimension. A model of the crack-tip slip bands blocked by the grain boundary was confirmed to be useful for analysing very slow growth as well as the threshold condition. The shear-mode fracture surface observed on the surface in region A1suggests the repeated nucleation mechanism for crack growth. The effects of the stress ratio and the grain size on the crack closure behavior near the threshold was quantified.     

Propagation of stress corrosion cracks in aligned glass fibre composite materials

A modified fracture toughness test has been used to measure the growth of cracks in unidirectional glass fibre/polyester resin composite materials in the presence of a dilute hydrochloric acid. Crack growth rates perpendicular to the fibre axis have been measured over a range of stress intensities. Scanning electron microscope studies of the fracture surfaces have shown that the micromechanisms of nucleation and propagation are dependent on stress intensity. The use of crack growth data to predict component lifetimes and the existence of inherent flaws in the material are discussed.     

Dynamic fracture (spalling) of metals

The fundamental mechanical aspects of dynamic fracture in metals are presented, with emphasis on spalling produced by the interactions of shock and reflected tensile waves. The major research efforts conducted in this area are reviewed; the process has been successfully described as a sequence of nucleation—growth—coalescence of voids or cracks. Quantitative models predicting the extent of damage have been successfully compared with experimental observations, by incorporating them into computer codes.A number of metallurgical aspects of importance are discussed: failure initiation sites, crack propagation paths, strain-rate-dependent ductile to brittle transition, grain size effect, intergranular versus transgranular spalling. Of particular importance in iron and steels is the change in spall morphology when the 13 GPa stress is exceeded. This change is documented and interpreted in terms of the α(BCC)→?(HCP) phase transformation undergone at that pressure. Micromechanical models describing the growth of voids in terms of dislocation motion are discussed.Areas requiring additional research effort are identified.     

Challenges in Continuum Modelling of Intergranular Fracture

Abstract: Intergranular fracture in polycrystals is often simulated by finite elements coupled to a cohesive zone model for the interfaces, requiring cohesive laws for grain boundaries as a function of their geometry. We discuss three challenges in understanding intergranular fracture in polycrystals. First, 3D grain boundary geometries comprise a five‐dimensional space. Second, the energy and peak stress of grain boundaries have singularities for all commensurate grain boundaries, especially those with short repeat distances. Thirdly, fracture nucleation and growth depend not only upon the properties of grain boundaries, but also in crucial ways on edges, corners and triple junctions of even greater geometrical complexity. To address the first two challenges, we explore the physical underpinnings for creating functional forms to capture the hierarchical commensurability structure in the grain boundary properties. To address the last challenge, we demonstrate a method for atomistically extracting the fracture properties of geometrically complex local regions on the fly from within a finite element simulation.     

Characterization of 2-dimensional crack propagation behavior by simulation and analysis

Crack propagation behavior in 2-dimensional polycrystals is simulated and analyzed as a function of the fracture toughness of the grain boundary. The path of a crack impinging on a grain boundary is determined by the competition theory between intergranular and transgranular propagation. With decreasing boundary toughness, the tendency of intergranular propagation increases and the apparent fracture toughness of the polycrystal decreases. The results of the 2-dimensional analysis are compared with the simulation, and the advantages and limitations are discussed. The grain boundary toughness is evaluated by comparing the simulated crack paths with direct observations, resulting in a reasonable value for alumina ceramics. The fracture behavior is characterized in a macro-scale by the percentage of transgranular fracture and also in a micro-scale by the distribution of crack deflection angles.     

Internal strain energy and the strength of brittle materials

The theory of Clarke for the formation of grain boundary cracks in anisotropic polycrystalline materials, is re-examined in the light of recent experimental data. The theory predicts correctly the conditions for the formation of grain boundary cracks of length similar to a grain dimension. However, the theory cannot be used to explain the experimentally observed strength/grain size and strength/irradiation dose relationships, for example for BeO. The theory supposes that the process controlling catastrophic fracture is the growth of a crack from a grain boundary pore with an energy absorption rate corresponding to the grain boundary surface energy of 10³ erg/cm². In practice, the process controlling catastrophic fracture is the subsequent growth of a crack from a grain dimension, with a higher energy absorption rate corresponding to an effective surface energy of 10⁴ erg/cm².     

Spall experiments for the measurement of the tensile strength and fracture energy of concrete at high strain rates

To study the behavior of concrete under dynamic loads, a Hopkinson-Bar was set up and used. Cylindrical concrete specimens were positioned at the end of the incident bar and the spall event was studied. The purpose of this contribution is to explain the measurement of the tensile strength and the specific fracture energy. To determine the tensile strength, the measured free surface velocity at the end of the specimen is used. The method is known from plate impact experiments and was adapted to Hopkinson-Bar experiments. The measurement of the specific fracture energy is more difficult in spall experiments. It cannot be measured directly as it can be done in direct tension tests. A method is proposed where the fracture energy is calculated from the change of the fragment velocities while cracking takes place.The experimental results of the investigation complete the data of the literature in regard to higher strain rates. In former investigations conducted by Weerheijm (PhD thesis. Delft University of Technology: Delft University Press; 1992), an increase of the specific fracture energy with the strain rate or the crack opening velocity was not seen. The experiments performed within this contribution consider the fracture behavior at higher strain rates. A sharp increase in the specific fracture energy at this strain rates was measured. The following paper describes the method and the experiments to measure the tensile strength and the specific fracture energy in spall experiments.     

NUCLEATION AND SHORT CRACK GROWTH IN FATIGUED POLYCRYSTALLINE COPPER

Surface evolution in polycrystalline copper specimens with a shallow notch has been studied in interrupted constant strain amplitude cyclic loading. The inhomogeneous strain distribution close to stress amplitude saturation leads to the formation of extrusions and intrusions along persistent slip bands within the grain and also in suitably oriented grain boundaries. Numerous primary cracks within a grain or at a grain boundary are nucleated. Some cracks can grow further either by linking with existing cracks or by nucleation of new elementary cracks ahead of the crack tip. Crack growth rates of individual cracks fluctuate considerably but for each strain amplitude, which results in a saturated plastic strain amplitude, a crack growth rate of an equivalent crack can be established. This crack growth rate was found to depend strongly on the plastic strain amplitude in agreement with the Manson-Coffin law.     

Ductile failure analysis and crack behavior of X65 buried pipes using extended finite element method

This paper aims to study the ductile fracture mechanism of API X65 buried pipes including crack initiation and propagation using the extended finite element method (XFEM). First, the crack evolution histories of X65 specimens with initial crack-like flaws during tensile and three-point bending tests are illustrated, and the numerical results are compared with experimental data. In addition, effects of different crack configurations, damage initiation and evolution criteria are investigated. Second, the burst processes of straight pipes with initial gouge flaws are presented, and the FE results are compared with assessment in related standards and experiments. Finally, the crack onset and growth of buried pipes due to deflection arising from landslide movements are predicted, and the numerical results are compared with previous study. Particularly, the internal pressure, wall thickness, and soil properties on crack behavior and limit load-bearing ability are investigated. This paper provides a fundamental support for the integrity assessment and safety evaluation of buried pipes.     

SMALL FATIGUE CRACKS IN AN AUSTENITIC STAINLESS STEEL

The present study concerns nucleation and growth of small surface cracks during the low-cycle fatigue of a nitrogen-containing austenitic stainless steel. Metallographic replicas as well as longitudinal sectioning were used to record the developing crack pattern on the specimen surface. The influence of grain size and nitrogen content is considered. Small surface cracks are observed after about 10% of the fatigue life. The nucleation of cracks continues until about half of the lifetime, when the crack density saturates. This saturation phenomenon is related to the local unloading effect of growing cracks.
The mean crack length increases continuously as a power-law until specimen failure. However, small grains and a low nitrogen content amplify the effect of crack–grain boundary interactions resulting in an intermediate retardation in growth.
At high nitrogen contents, the crack growth characteristics are very much related to the slip bands formed. This results in a more simultaneous growth of cracks, a more jagged feature of the cracks introducing a higher roughness-induced crack closure effect, and, consequently, better fatigue properties.