Crack Tip Shielding Research Articles

Toughening materials: enhancing resistance to fracture.

It has been said that 'God invented plasticity, but the Devil invented fracture!' Both mechanisms represent the two prime modes of structural failure, respectively, plastic collapse and the rupture/breaking of a component, but the concept of developing materials with enhanced resistance to fracture can be difficult. This is because fracture resistance invariably involves a compromise-between strength and ductility, between strength and toughness-fundamentally leading to a 'conflict' between nano-/micro-structural damage and the mechanisms of toughening. Here, we examine the two major classes of such toughening: (i)intrinsic toughening, which occurs ahead of a crack tip and is motivated by plasticity-this is the principal mode of fracture resistance in ductile materials, and (ii) extrinsic toughening, which occurs at, or in the wake of, a crack tip and is associated with crack-tip shielding-this is generally the sole mode of fracture resistance in brittle materials. We briefly examine how these distinct mechanistic processes have been used to toughen synthetic materials-intrinsically in gradient materials and in multiple principal-element metallic alloys with the example of metallic glasses and high-entropy alloys, and extrinsically in ceramics with the example of ceramic-matrix composites-in comparison to Nature which has been especially adept in creating biological/natural materials which are toughened by one or both mechanistic classes, despite often consisting of constituents with meagre mechanical properties. The success of Nature has been driven by its ability to cultivate the development of materials with multiple length-scale hierarchical structures that display ingenious gradients and structural adaptability, a philosophy which we need to emulate and more importantly learn to synthesize to make structural materials of the future with unprecedented combinations of mechanical properties. This article is part of a discussion meeting issue 'A cracking approach to inventing new tough materials: fracture stranger than friction'.

Quasi-static and dynamic fracture behavior of lead zirconate titanate: A study of poling and loading rate

In this study, coupon specimens of both poled and de-poled lead zirconate titanate (PZT) are examined under quasi-static and stress-wave loading conditions. Mode-I crack initiation and fracture behavior is examined using ultra high-speed imaging in conjunction with 2D digital image correlation on symmetrically impacted specimens. Measured displacement fields ahead of the dynamically loaded crack tip are used to extract the critical stress intensity factor (KICd) at initiation and are compared with quasi-static SENT fracture toughness tests. Results demonstrate that under static conditions, the difference between poled and de-poled specimens is not statistically significant, however under dynamic conditions, poled samples exhibited a 70% greater fracture toughness compared to the de-poled specimens. To verify the increase was not due to thermal degradation of material mechanical properties during the de-poling process, re-poled specimens were also prepared and examined under dynamic fracture loading conditions. In general, impulsively loaded samples exhibited greater fracture toughness compared to their quasi-statically loaded counterparts, regardless of the poling. Specifically, the critical stress intensity factor increased seven to tenfold compared to static fracture toughness values, with poled samples exhibiting the greatest toughness of all samples explored. In terms of rate, the increase in fracture toughness under dynamic conditions likely comes from microcracking and potentially phase transformations at the crack tip. In terms of poling, the increase in fracture toughness is likely due to a bulk manifestation of ferroelastic toughening, where dynamic domain reorientation provides crack tip shielding.

Effect of Solution Annealing on Fatigue Crack Propagation in the AISI 304L TRIP Steel.

Fatigue crack propagation in near-threshold regime was studied in the 304L austenitic stainless steel in two microstructural states: as-received (AR) with finer microstructure and low susceptibility to the transformation-induced plasticity (TRIP) effect, and solution-annealed (SA) with coarser microstructure and higher susceptibility to TRIP. At the load ratio R = 0.1 the threshold was higher in the SA state than in the AR state due to coarser grains and possibly the TRIP effect. In order to clarify the role of crack closure, experiments at R = 0.7 were done. The threshold in the SA state was still higher by 1 MPa·m0.5. This effect was identified as crack tip shielding induced by phase transformation, an example of a non-closure shielding effect. Higher resistance to crack growth in the SA state was attributed to promoted martensitic transformation in non-favorable oriented grain families rather than thicker martensite layers in the crack path area. The conclusions were verified by experiments at R = 0.7 and temperature 150 °C > Ms which did not reveal any notable difference in thresholds. However, the threshold values were affected by the load-shedding gradient C = −dΔK/da, which had to be equalized in both experimental setups inside and outside the furnace.

Transformation toughness induced by surface tension of the crack-tip process zone interface: A field-theoretical approach.

We study a crystal with a motionless crack exhibiting the transformational process zone at its tip within the field-theoretical approach. The latter enables us to describe the transformation toughness phenomenon and relate it to the solid's location on its phase diagram. We demonstrate that the zone extends backward beyond the crack tip due to the zone boundary surface tension. This setback engenders the crack-tip shielding, thus forming the transformation toughness. We obtain a quadrature expression for the effective fracture toughness using two independent approaches-(i) with the help of the elastic Green function and, alternatively, (ii) using the weight functions-and calculate it numerically applying the results of our simulations. Based on these findings, we derive an accurate analytical approximation that describes the transformation toughness. We further express it in terms of the experimentally accessible parameters of the phase diagram: the hysteresis width, the phase transition line slope, and the transformation strain.

Mechanical Properties of Epoxy/Clay Composite Coatings on an X65 Steel Substrate

This paper presents the results of a combined experimental and theoretical study of the interfacial and mechanical properties of epoxy/clay composites coatings on a mild steel substrate. This was studied using nano-indentation and Brazil Disk techniques to determine the Young’s moduli, hardness values and mode mixity characteristics of the composite coatings. The Young’s moduli of the reinforced composites comprising 1, 3, and 5 wt. % of montmorillonite clay particles are shown to improve, respectively, by about 23%, 58%, and 50% while the respective hardness values increased by about 46%, 80%, and 88%, relative to those of pristine epoxy. The measured mechanical properties have also shown to compare favorably with predictions from composite theories (rule-of-mixture and shear lag theories). The interfacial toughness between X65 steel and the epoxy/clay coatings increases with increasing mode mixity. This is associated with crack-tip shielding by crack deflection and crack bridging. The trends in the measured mode-mixity dependence of the interfacial fracture toughness values are consistent with predictions from the simplified zone, normal zone, and row models (at lower mode mixity). The insights from the observations and the measured crack profiles are incorporated into zone and row models for the estimation of crack-tip shielding. The implications of the results are discussed for the design of epoxy/clay composites with attractive combinations of mechanical properties.

Two-scale porosity effects on cohesive crack growth in a ductile media

Microstructures with two distinct size-scales of voids are commonplace in additively-manufactured metals. The smaller-scale voids nucleate from inclusions within the metal, while the larger-scale voids originate from unsintered powder particles. In this work, we study the interaction between these two size-scales of voids ahead of a crack, and the influence on the ductile fracture process. We adopt a finite element model of a centerline crack subjected to small-scale yielding conditions. The diffuse process zone ahead of the crack is modeled by several rows of void-containing cell elements governed by a Gurson porous material relation. Results show that the larger-scale voids near the initial crack tip generally reduces the fracture toughness by facilitating void coalescence with the crack-tip to form a single contiguous damage zone. However, strategic placements of these larger-scale voids within the active plastic zone of the crack-tip can promote crack-tip shielding, leading to diffused damage in the form of multiple unconnected damage zones, and ultimately, a several-fold improvement in toughness. We quantify the fracture behavior, as a function of the relative size and proportion of larger-scale voids in the diffuse process zone, by reconstructing the equivalent crack-tip cohesive zone laws in an elasto-plastic medium via nonlinear field projection. We demonstrate that the cohesive strength, cohesive energy, as well as the functional form of the cohesive zone law, are strongly dependent on the dual void size-scales, which introduces a size-effect into the homogenized traction-separation relationship.

Effects of grain size on fatigue crack growth behaviors of nanocrystalline superelastic NiTi shape memory alloys

The grain size (GS) dependence of fatigue crack growth in nanocrystalline superelastic NiTi shape memory alloys (SMAs) with the average GS of 10, 30, 60 and 235 nm is investigated. Synchronized measurements of the fatigue crack growth, load-displacement response and temperature field of the compact tension specimens are performed. It is found that the fatigue crack growth rate (da/dN) is monotonically decreased by 10 times when the GS is increased from 10 to 235 nm. The significant GS effect on the fatigue crack growth is also confirmed by the direct observation of fatigue striation spacing on the postmortem fracture surface. It is shown that the increase of the GS significantly enhances the phase transition and plasticity of the material and therefore enhances the crack-tip shielding (Ksh) which reduces the effective driving force (ΔKeff) of the fatigue crack growth. Subtracting Ksh due to phase transition and plastic deformation from the external applied Kapp, the effective crack-tip fatigue driving force ΔKeff is obtained. The da/dN-ΔKeff curves for different GS specimens then almost collapse onto a single curve which may represent an intrinsic fatigue property of the NiTi in the absence of the shielding effects. Therefore the observed apparent GS dependence of the fatigue crack growth resistance in the superelastic NiTi SMAs is mainly caused by the shielding effect from the GS dependent phase transition and plastic deformation.

Mode II crack shielding in a compressed rough crack with friction

In this paper, a two-dimensional model to describe the non-planar geometrical features of crack morphologies is presented. The model accounts for frictional tractions along the crack surfaces by considering a rigid-plastic constitutive interface law. Dilatancy effect due to crack roughness is described by the model, leading to a Mode I/II coupling between displacements and tractions along the crack surfaces. The non-linear solution of the rough and frictional crack under general remote loading paths is obtained using the Distributed Dislocation Technique (DDT). By considering a linear piecewise periodic profile of the interface crack, the influence of roughness and friction of an edge crack is examined in relation to both the resulting near-tip stress field and the fracture resistance under monotonic mixed-mode loading. The present model is capable of quantifying the increase of the fracture resistance due to roughness- and friction-induced crack tip shielding.

Near-tip strain evolution and crack closure of growing fatigue crack under a single tensile overload

Fatigue crack growth retardation of AZ31 alloy under a single tensile overload was investigated by 3D synchrotron radiation, 2D in-situ SEM and digital image correlation techniques. Results showed a consistent evolution of crack closure level by both 3D and 2D methodologies. The straining and plastic zone ahead of crack-tip, and crack opening displacement behind, which were quantitative indicators of crack-tip shielding, residual stress formation and relaxation, were correlated well with the retardation behavior. Mechanistically, compressive residual stress played a dominant but time-limited role while crack closure was secondary, based on an intrinsic load transfer concept during crack growth.

On the role of anisotropic expansion and yield stress on crack tip precipitates

This pilot study uses a Landau-Lifshitz phase field model to study the growth of a precipitate originating from a crack tip. A boundary layer giving a remote square root singular elastic stress field is applied. The materials are assumed to be elastic-plastic with linear strain hardening. The precipitate is assumed to expand in a simplified anisotropic manner, meaning that the hydride is assumed to grow with an orientation giving maximum expansion perpendicular to the crack plane. The results show that the anisotropic expansion has a strong effect on the shape of the hydride. For anisotropic materials the hydride becomes wedge like. The resulting shapes for the anisotropic cases are in line with observations of internal crack tip hydrides in zirconium. The shapes resemble earlier results for Einstein-Smoluchowski stress driven diffusion using discrete models and simplified modelling of the growth process. The crack tip shielding caused by both precipitation and plastic yielding is examined using the J integral. It shows that the near tip value is a around a quarter of its remote value for elastic isotropic materials and around a half for anisotropic materials.

Temperature dependent fracture toughness of KNN-based lead-free piezoelectric ceramics

The fracture toughness of unpoled and electrically poled lead-free KNN-based piezoelectric ceramics with the composition of 0.92KNN-0.02Bi0.5Li0.5TiO3-0.06BaZrO3 was investigated. Results reveal that at room temperature, the intrinsic fracture toughness (KI0) of the unpoled samples, evaluated by the near-tip crack opening displacement (COD) technique, is the lowest with a value of 0.70 MPa⋅m0.5; the long (through-thickness) crack fracture toughness (KIvnb), obtained by the single edge V-notch beam (SEVNB) technique, is the highest, with a value of 0.95 MPa⋅m0.5; intermediate short surface crack fracture toughness (KIsc) of 0.86 MPa⋅m0.5 was determined by the surface crack in flexure (SCF) technique. These results were rationalized by the toughening behavior of the material combined with the crack geometry-dependent stress intensity evolution during crack propagation. With increasing temperature, KIvnb and KIsc decrease, and become nearly identical at 350 °C, suggesting an absence of toughening. For electrically poled samples, their room temperature fracture toughness was characterized by both SCF and SEVNB techniques, with values of 0.88 MPa⋅m0.5 and 0.99 MPa⋅m0.5, respectively, slightly larger than the values measured for unpoled samples. Nonlinear electric field-strain and stress-strain analysis of the material was also employed during electric field loading, mechanical compression and four-point bending in order to quantify crack tip shielding by domain switching and the actual stress at the point of instable crack propagation.

Glass ionomer cements with enhanced mechanical and remineralizing properties containing 45S5 bioglass-ceramic particles

The clinical applications of glass ionomer cements (GICs) are limited by their relatively poor mechanical properties and insufficient remineralizing capacity. In this study, we developed hybrid GICs with improved mechanical and remineralizing properties via incorporation of an optimum amount (5 wt%) of 45S5 bioglass-ceramic particles. Also, we found that bioglass-ceramic particles with 74% crystallinity best act as both remineralizing and reinforcing agents. The degree of crystallinity of the additives, is overlooked in this context in other research. At around 74% crystallinity, there is sufficient amount of combeite and an amorphous phosphorous-rich phase in the 45S5 bioglass-ceramic particles to respectively promote their reinforcing role and allow them to effectively partake in the setting process creating an excellent interfacial bond with the GIC matrix. As a result, several strengthening mechanisms such as crack deflection and crack-tip shielding are activated within the hybrid GIC containing 5 wt% bioglass-ceramic with 74% crystallinity, contributing to its improved mechanical properties. The enhanced remineralizing and mechanical properties of such hybrid GICs can potentially improve their in vivo performance and broaden their clinical applications.

On the formation of expanding crack tip precipitates

The stress driven growth of an expanding precipitate at a crack tip is studied. The material is assumed to be linearly elastic, and the expansion is considered to be isotropic or transversely isotropic. The extent of the precipitate is expected to be small as compared with the crack length and distance to boundaries. The problem has only a single length scale given by the squared ratio of the stress intensity factor and a critical hydrostatic stress that initiates the growth of the precipitate. Therefore, the growth occurs under self-similar conditions. The equations on non-dimensional form show that the free parameters are expansion strain, degree of anisotropy and Poisson’s ratio. It is found that the precipitate, once initiated, grows without remote load for expansion strains above a critical value. The anisotropy of the expansion strongly affects the shape of the precipitate but does not have a large effect on the crack tip shielding.

Temperature Dependent Fracture Toughness of KNN-Based Lead-Free Piezoelectric Ceramics

The fracture toughness of lead-free KNN-based piezoelectric ceramics with the composition of 0.92KNN-0.02Bi0.5Li0.5TiO3-0.06BaZrO3 was investigated by near-tip crack opening displacement (COD), surface crack in flexure (SCF), as well as single edge V-notch beam (SEVNB) techniques. Results reveal that the intrinsic fracture toughness (KI0), evaluated by the COD technique, is the lowest with a value of 0.70 MPa∙m0.5. The long (through-thickness) crack fracture toughness (KIvnb), obtained by the SEVNB technique, is the highest, with a value of 0.95 MPa∙m0.5. Intermediate short surface crack fracture toughness (KIsc) of 0.86 MPa∙m0.5 was determined by the SCF technique. These results were rationalized by the toughening behavior of the material combined with the crack geometry-dependent stress intensity evolution during crack propagation. With increasing temperature, KIvnb and KIsc decrease. At 350 °C, they are nearly identical, suggesting an absence of toughening. Nonlinear stress-strain analysis of the material was also employed during compression and four-point bending in order to quantify crack tip shielding by domain switching and in order to quantify the actual stress at the point of instable crack propagation.

Fracture toughening of peritubular microstructure in biological porous dentine

Fracture behavior of biological porous dentine is important to the success of dental restoration. The role of peritubular dentine (PTD) microstructure on the fracture properties of human dentine is investigated by analysis of its crack tip shielding effect on microcracks and macrocracks. The evolution of microcracks around the dentine tubules (DTs) and the growth of macrocracks in the dentine are experimentally observed by scanning electron microscope. Two cases of an individual PTD&DT penetrating the microcrack tip and locating ahead of the microcrack tip are discussed. The effects of multiple PTD&DTs with random distribution and various porosities on the macrocrack shielding or amplifying in dentine are also particularly investigated. The importance of modulus, thickness of PTD and porosity of DT to the shielding effect of crack growth in dentine is studied by finite element analysis, which is characterized by the dominated fracture parameter J-integral. Numerical results demonstrate that PTD can shield the growth of dentine microcracks. When the PTD is in a specific location around macrocracks, it also has a shielding effect. The thicker and harder the PTD, the greater the shielding effect on crack growth. In conclusion, the porous dentine can be used as a reference structure in the design of implant dentures to enhance the dentine toughness.

Characterisation of fatigue crack growth using the CJP model of crack tip fields or plastic CTOD

This paper provides an update on the current status of work that has been done to validate the CJP model of crack tip stresses and also summarises some findings from linked work that has used DIC to determine the range of plastic crack tip opening displacement as a correlator of fatigue crack growth rate. The paper considers several ways of calculating an effective range of stress intensity factor that have been proposed in various papers, as the preferred option is not yet fully clear. It further highlights the potential value, in terms of elucidating the mechanisms involved in plasticity-induced crack tip shielding, arising from data obtained from using two different DIC techniques on the same specimens.

Crack shielding in non-planar and frictional discontinuities under mixed-mode loading

In this paper, a two-dimensional model to describe the non-planar features of crack morphologies is presented. The model accounts for frictional tractions along the crack surfaces by considering an elastic-plastic-like constitutive interface law. Dilatancy effect due to crack roughness is described by the model, leading to a Mode I/II coupling between displacements and tractions along the crack surfaces. The non-linear solution of the rough and frictional crack under general remote scenarios is obtained using the Distributed Dislocation Technique (DDT). By considering a linear piecewise periodic profile of the interface crack, the influence of roughness and friction of interface cracks is examined in relation to both the resulting near-tip stress field and the fracture resistance under monotonic mixed-mode loading. The present model is able to quantify the increase of the fracture resistance due to roughnessand friction-induced crack tip shielding and to correlate it with a dimensionless crack size parameter.

Crack dynamics and crack tip shielding in a material containing pores analysed by a phase field method

Many naturally occurring materials, such as wood and bone, have intricate porous micro-structures and high stiffness and toughness to density ratios. Here, the influence of pores in a material on crack dynamics in brittle fracture is investigated. A dynamic phase field finite element model is used to study the effects of pores with respect to crack path, crack propagation velocity and energy release rate in a strip specimen geometry with circular pores. Four different ordered pore distributions are considered, as well as randomly distributed pores. The results show that the crack is attracted by the pores; this attraction is stronger when there is more energy available for crack growth. Crack propagation through pores also enables higher crack propagation velocities than are normally seen in strip specimens without pores (i.e. homogeneous material), without a corresponding increase in energy release rate. It is further noticed that as the porosity of an initially solid material increases, the crack tip is increasingly likely to become shielded or arrested, which may be a key to the high relative strength often exhibited by naturally occurring porous materials. We also find that when a pore is of the same size as the characteristic internal length then the pore does not localise damage. Since the characteristic internal length only regularises the damage field and not the strain end kinetic energy distributions, crack dynamics are still affected by small pores.

Retardation of Small Creep–Fatigue Crack in Gr. 91 Steel Through the Combined Effects of Stress Relaxation, Microstructural Evolution, and Oxidation

This investigation reports an unusual effect of hold time (up to 10 seconds) on retardation in the growth of creep–fatigue small cracks at 550 °C in Grade 91 steel. The observed phenomenon was interpreted by elucidating multiple processes that are active in the plastic zone at the crack tip. To this effect, microstructural and mechanical responses of the crack tip plastic zone were compared with the mechanical and microstructural responses during low cycle fatigue/creep–fatigue. It is proposed that the stress relaxation that occurs during the hold time can reduce the stress intensity in the plastic zone of crack tip thus, contributing to retardation in the small crack growth rate. Aside from stress relaxation, stress intensity in the crack tip can be further reduced by the phenomenon of cyclic softening that occurs because of plasticity-induced microstructural coarsening. Separately, the contribution of oxidation-induced crack tip shielding is also considered to explain the observed effects of hold time on crack growth rates. Taken together, a combination of stress relaxation, enhanced rate of cyclic softening, and higher degree of oxidation with the introduction of a hold time is demonstrated to be responsible for reduction in the crack growth under creep–fatigue conditions.

Dislocation shielding at elevated temperatures in pre-cracked microscale silicon

Increasing evidence demonstrates that some ceramics and semiconductors can possess increased ductility and fracture toughness at lower temperatures than previously thought. The present study focuses on the unlikely candidate of single-crystal silicon, which is studied using microscale bending beams at elevated temperature. A potential solution for the issue of focused ion beam (FIB) pre-notches is also presented, by re-propagating arrested cracks. This allows for proper measurement of stress intensity from nearly atomically sharp cracks, along with removing any potential influence of Gallium. This does not mean the crack is initially dislocation free but does represent an appropriate microstructure that might be experienced in a manufacturing setting. Through post mortem transmission electron microscopy (TEM) of thinned samples after testing between 300 and 873 K, dislocation nucleation is observed at temperatures near 500 K. Beyond 500 K, there is increased propensity toward dislocation enhanced toughening through either crack-tip shielding and/or generalized plasticity.