Damage Nucleation Research Articles

Effect of Texture on the Fatigue Crack Initiation of a Dual-Phase Titanium alloy

Fatigue indicator parameters (FIPs) can serve as a measure of fatigue crack initiation (FCI) in metals and alloys. FIPs are volume averaged over grains, bands, and sub bands in crystal plasticity (CP) simulation to investigate the influence of texture on FCI under low cycle fatigue. The equiaxed microstructure of Ti-6Al-4V was generated with three different textures: basal, basal/transverse and transverse. FIPs analysis shows that basal texture has the highest FCI resistance, basal/transverse texture has intermediate resistance, and transverse texture has the lowest resistance. All textures exhibit a lower FIP when deformed along rolling direction (RD) than that along transverse direction (TD). The interior of the alloys has a larger FCI resistance than the free surface. Further analysis shows a strong relationship between FIP distribution features and damage nucleation characteristics, with basal texture exhibiting the lowest and wider FIP distributions as a result of high resistance to damage and fatigue cracking; in contrast, the transverse texture exhibits intense and narrow FIP and damage nucleation along the grain boundaries (GBs), basal/transverse texture exhibits FIP and damage nucleation with mixed characteristics. The results can be used as a theatrical reference for the fatigue performance of Ti alloy design.

Microstructure and stress mapping in 3D at industrially relevant degrees of plastic deformation

Strength, ductility, and failure properties of metals are tailored by plastic deformation routes. Predicting these properties requires modeling of the structural dynamics and stress evolution taking place on several length scales. Progress has been hampered by a lack of representative 3D experimental data at industrially relevant degrees of deformation. We present an X-ray imaging based 3D mapping of an aluminum polycrystal deformed to the ultimate tensile strength (32% elongation). The extensive dataset reveals significant intra-grain stress variations (36 MPa) up to at least half of the inter-grain variations (76 MPa), which are dominated by grain orientation effects. Local intra-grain stress concentrations are candidates for damage nucleation. Such data are important for models of structure-property relations and damage.

A Multiscale Inelastic Internal State Variable Corrosion Model.

We present a corrosion internal state variable (ISV) damage model based upon the integrated computational materials engineering (ICME) hierarchical multiscale paradigm. Structure-property experiments for magnesium alloys were used where the only inputs were the volume fractions of each element of the periodic table. This macroscale ISV corrosion model finds its basis in Horstemeyer's mechanical damage model, which includes three separate ISVs for damage nucleation, growth, and coalescence, as well as Walton's inclusion of corrosion, which introduces five new ISVs for pit nucleation, growth, and coalescence, along with general corrosion and intergranular corrosion. While Walton's corrosion ISVs are phenomenological in nature, herein we develop a multiscale physical basis for the corrosion ISVs. The parameters for the macroscale corrosion ISVs were garnered from the mesoscale Butler-Volmer equations. Pure magnesium with differing amounts of aluminum were used in corrosion tests to exemplify the different pitting, general corrosion, and intergranular corrosion rates, and the macroscale ISV model was calibrated with said data, in which the only inputs to the model are the volume percentages of the elements magnesium and aluminum. Although magnesium alloys were used to motivate and calibrate the model, the model is abstract enough to possibly capture other material systems as well.

Ductile shear damage micromechanisms studied by correlative multiscale nanotomography and SEM/EBSD for a recrystallized aluminum alloy 2198 T8

The damage mechanisms of ductile fracture under shear loading of an aluminum alloy 2198T8R were studied using flat thin-sheet samples. One sample was loaded until 85% of the failure displacement and then unloaded, and another one was loaded up to failure. To overcome the inherent shortcomings of nanotomography concerning the investigation of flat samples, synchrotron nano-laminography was applied to the pre-loaded sample and provided structural information down to the nanometer scale, allowing ductile damage nucleation and evolution to be studied. The damage features, including flat cracks and intermetallic particle-related damage, were visualized in 3D from the highly-deformed shear band region. Using nano-laminography, no nano-voids were found. The damaged shear ligament was also observed after polishing via destructive correlative scanning electron microscope (SEM) and electron back-scatter diffraction (EBSD) which suggests that the detrimental flat cracks were both intergranular and transgranular. The flat cracks were related to highly-deformed bands. No nano-voids could be found using SEM analysis. Fractography on the second broken sample revealed that the flat cracks contained hardly observable nanometer-sized dimples. The final coalescence region was covered by sub-micrometer-sized dimples, inside which dispersoid particles were present. The fact that no nano-void was found for the pre-deformed sample implies that the nucleation, growth and coalescence of these sub-micrometer-sized voids occur at late stages of the loading history.

Continuum Model of Peridynamics for Brittle Fracture Problems

The article investigates the nonlocal method of peridynamics, which makes it possible to simulate the brittle fracture of a solid body without using spatial derivatives. The basic motion equation of a particle with a given volume is written in integral form. A model combining the key features of continuum mechanics and of the nonlocal method is considered. To determine the forces of pair interaction, the dependence of the Cauchy stress tensor on the rate-of strain tensor was used. This formulation correctly describes the behavior of the material during damage and allows to get rid of the limitations inherent to simple bond-based model and ordinary state-based model. The maximum value of the tensile stress is used as a criterion of fracture, which describes the process of nucleation and evolution of damage. To test the implemented model, tasks in a two-dimensional formulation were used. Using the example of the elastic problem about uniaxial tension of a thin rod, the convergence of the numerical solution is shown with a decrease of interaction horizon and an increase of particles number. The second task demonstrates the capabilities of the implemented model to describe the nucleation and evolution of a crack under uniaxial load on a plate with an initial horizontal defect.

Cyclic damage quantification in composite materials using discrete damage mechanics

A method for fatigue damage quantification in composite materials, based on experimental stiffness degradation data for composite laminates subjected to cyclic load is proposed. Discrete damage mechanics theory is used to calculate crack density vs. number of cycles from elastic moduli-reduction data obtained during fatigue experiments. The calculated crack density simplifies fatigue testing by diminishing the need for counting cracks during testing. Accurate results are achieved and reported. The defect-nucleation rate, which controls the fatigue damage rate, is also obtained from processing the modulus-reduction data. It is observed that the defect-nucleation rate has a small scatter and is independent of applied load magnitude. Furthermore, the onset of delamination observed in the experiments correlates very well with the onset of deviation between the predicted and experimental curves of elastic moduli-reduction versus accumulated crack density. An additional parameter, the defect-nucleation threshold, is here proposed to further characterize the fatigue performance of the composite material under stress-controlled fatigue loading, in contrast to thermal fatigue results from the literature. Furthermore, the difference in damage nucleation rate between strain-controlled and stress-controlled was observed and discussed.

In-situ deformation inhomogeneity and damage evolution of mixed-grain structure with tempered sorbite/bainite in Fe–Cr–Mo–Mn steel

The inhomogeneous tempered sorbite/bainite (TS/B) with various morphologies and orientations play a significant role in deformation coordination and damage evolution. In this paper, the influence of distinct morphologies and orientations of the mixed-grain structure with TS/B on the deformation heterogeneity were extensively investigated by in-situ tensile testing. Furthermore, a multi-scale model of dislocation density-based crystal plasticity (CP) coupled with the phase field method (PFM) was developed to illustrate the damage nucleation and its evolution via the representative volume element (RVE) modelling. The results shows that mixed-grain structure with TS/B exhibits non-homogeneous deformation during the tensile process, and the coarse grains bear the main plastic deformation, resulting in cross-slip traces and the wrinkling phenomenon at the grain boundary and the interior of coarse grains. Furthermore, the activation of slip systems was determined through slip trace analysis, and the slip transfer behavior between adjacent microstructure was analyzed. According to the critical resolved shear stress (CRSS), the {123}<111> slip system was determined to be the most activated slip system during the in-situ deformation. Hard-orientated lath-shaped B (M1) is more prone to accumulate low angle grain boundaries (LAGBs) than hard-orientated TS (M2) and soft-orientated granular B (M3), resulting in higher orientation rotation degree and geometrically necessary dislocations (GNDs) density of M1 than M2 and M3. The M1 exhibits the nucleation of damage during the initial deformation stage. In addition, compared with the M2 and M3, the Schmid factor (SF) of M1 dominates the transformation from hard orientation to soft orientation and the higher value of damage factor (φ) of M1 results in the more activated slip systems and local damage at high strain levels. This study provides new insights into elucidate the effects of TS/B morphologies and orientations on deformation heterogeneity and damage evolution in large-scale forged spindles for offshore wind power.

Ductile Fracture of Titanium Alloys in the Dynamic Punch Test

Estimates of physical and mechanical characteristics of materials at high strain rates play a key role in enhancing the accuracy of prediction of the stress–strain state of structures operating in extreme conditions. This article presents the results of a combined experimental–numerical study on the mechanical response of a thin-sheet rolled Ti-5Al-2.5Sn alloy to dynamic penetration. A specimen of a titanium alloy plate underwent punching with a hemispherical indenter at loading rates of 10, 5, 1, and 0.5 m/s. The evolution of the rear surface of specimens and crack configuration during deformation were observed by means of high-speed photography. Numerical simulations were performed to evaluate stress distribution in a titanium plate under specified loading conditions. To describe the constitutive behavior and fracture of the Ti-5Al-2.5Sn alloy at moderate strain rates, a physical-based viscoplastic material model and damage nucleation and growth relations were adopted in the computational model. The results of simulations confirm a biaxial stress state in the center of specimens prior to fracture initiation. The crack shapes and plate deflections obtained in the calculations are similar to those observed in experiments during dynamic punching.

Shock and spallation behavior of ultrahigh molecular weight polyethylene

We investigate dynamic compression and fracture of ultra-high molecular weight polyethylene (UHMWPE) with plate impact experiments, high-speed velocimetry, and postmortem X-ray computed tomography. The Hugoniot equation of state of UHMWPE up to peak shock stress of ∼2.0 GPa is obtained via reverse impact. Spall strength and corresponding tensile strain rates are determined via symmetric impact. With increasing impact velocity, spall strength is nearly a constant (∼70 MPa) up at first, and then decreases continuously as a result of competition between increasing tensile strain rate, shock heating and strain softening; the damage degree increases first and then decreases rapidly at the expense of more damage nucleation sites. The void size distributions follow a power law. The small voids are closer to spheres and voids/cracks becomes flatter as void volume increases, likely because of the rearrangement and breakage of linear polymer chains of UHMWPE.

Dynamic spall properties of an additively manufactured, high-entropy alloy (CoCrFeMnNi)

The dynamic spall properties of an additively manufactured (AM), CoCrFeMnNi high-entropy alloy (HEA) were investigated as a function of processing defects. Laser Powder Bed Fusion (LPBF) was used to additively manufacture HEA samples that were subsequently subjected to shock loading through plate impact experiments. Seven different combinations of laser power and scan speeds were explored, ranging from 180 to 280 W and 925–1350 mm/s, respectively. All samples were considered within the bounds of lack-of-fusion and keyholing defects based on initial experiments, but exhibited varying degrees of solidification cracking and microstructural changes. Grain size and grain aspect ratio were found to modestly decrease with faster scan speeds and lower laser powers, while cracking associated with the AM process increased with faster scan speeds and higher laser powers. Spall strength and spall damage did not systematically trend with microstructural characteristics such as grain size, but did exhibit a relationship with pre-existing crack density. Spall properties were found to generally degrade with increasing crack density. Evidence of defect compaction was not observed in soft recovered spall samples, thus pre-existing cracks were proposed to degrade spall properties by acting as stress concentrators and preferred damage nucleation sites during tensile impact loading. Here, the presence of manufacturing-related defects, such as cracks, dominated the dynamic response; however, in the absence of these defects, microstructural changes like grain size and texture would be expected to control dynamic behavior.

Coupled diffusion-mechanical analysis with dislocation effect in porous spherical electrode

The electrochemical and mechanical performance of lithium-ion batteries is greatly affected by the porous electrode materials and dislocation effect. A diffusion-mechanical coupling model of porous electrode particle with dislocation effect is developed under potentiostatic operation in this work. Then, the distributions of lithium-ion concentration, volumetric strain and stress in the electrode particles with/without dislocation effect are analyzed. Finally, the influences of porosity and tortuosity on the lithium-ion concentration, volumetric strain, radial stress, hoop stress and strain energy are numerically discussed, respectively. The results show that dislocation effect retards the diffusion and relieves the electrode particle expansion and stresses. Moreover, larger porosity or smaller tortuosity can enhance the charge efficiency and avoid electrode particle damage or crack nucleation and propagation by reducing the stress and strain energy. Finally, from the perspective of fracture, dislocation effect can resist the crack propagation or avoid the formation of cracks during charge. This work will provide some theoretical guidance to improve the charge efficiency and prolong battery life.

Multi-scale spallation model for single-crystal ductile metals incorporating microscopic mechanism of void nucleation

Spall strength characterizes the tensile performance of materials under high strain rates. However, theoretical prediction of the spall strength has long been a big challenge since it involves information on the damage evolution at multiple length scales. In this work, a multi-scale model is proposed for the spallation of single-crystal ductile metals, which includes both a microscopic model of damage nucleation and an effective correlation between the microscopic physical mechanisms and the macroscopic mechanical behaviors. An energy criterion to predict the threshold stress for damage nucleation is firstly proposed based on a near-realistic three-dimensional configuration of dislocation emission. The statistical characteristics of the damage nucleation threshold are analyzed, based on which a multi-scale spall model is proposed to couple the physical essence at the micro-scale to the macro-scale, revealing the influences of temperature, vacancy concentration, and strain rate on spall strength. An approximate form of the multi-scale model is proposed by dimensional analysis and reasonable approximation, which is consistent with the empirical model summarized from experimental results, and further deduced to a simple scaling law that predicts the transition in the strain rate-sensitivity of spall strength.

A robust tension-compression asymmetric phase-field fracture model for describing PBX cracking under complex stress states

ABSTRACT The crack behaviors under complex stress states are very important for the safety of polymer-bonded explosives (PBXs) under accidental stimulations, but their accurate description is a challenge. Due to the advances of tracking discontinuities and multi-fields coupling, the phase-field model for complex fracture phenomena is attracting significant interest recently. Conventional phase-field fracture models are tension-compression symmetric or based on volumetric-deviatoric strain energy split, and these conventional phase-field models may lead to unrealistic fracture patterns, which hinders its further application in PBX fracture simulations. In this work, we present an extended, tension-compression asymmetric phase-field fracture model for PBXs, which distinguishes the contributions of tensile and compressive stresses to damage driving energy, and couples the mechanism of mechanical degradation and energy-driving cracking diffusion. We implemented our improved phase-field fracture model into finite element calculations and compared the simulation results with the conventional tension-compression symmetric phase-field fracture model and volumetric-deviatoric strain energy split phase-field fracture model by simulating PBX specimens under static loadings. The results show that our model not only accurately depicts the tensile and compressive cracks, but also describes compression-assisted cracking while suppressing unrealistic damage nucleation caused by small amplitudes of local compressive stresses, making it a very efficient way of describing PBX cracking under complex stress states. This new model is both mathematically and physically concise, and convenient for numerical implementation. Moreover, the novel model can be naturally extended to simulate shock-induced dynamic and/or coupled fracture of PBXs because of its feasibilities for dynamic extension and multi-field coupling.

In-situ study of damage mechanisms in Mg–6Li dual-phase alloy

Interfaces play a crucial role in influencing the mechanical properties of Mg alloys. For Mg–Li dual-phase alloy, the type of interfaces is complex, which includes both grain boundary and phase boundary, and the influence of such interfaces on the damage nucleation is yet to be explored. In this paper, in-situ scanning electron microscopy (SEM) based measurements were carried out to investigate the meso‑scale damage nucleation mechanisms of the Mg–6Li dual-phase alloy. Results show that 94.8% of cracks are nucleated at the α-Mg grain boundary in the post-uniform elongation stage, while 5.2% are at phase boundary and almost no crack at the β-Li grain boundary. The initiation of α-Mg grain boundary cracks is attributed to strain incompatibility, which induces micro-strain localization, and then causes grain boundary sliding (GBS) and crack nucleation. Deformation compatibility analysis reveals that the geometric compatibility factor (Mk) can be used to predict the nucleation of α-Mg grain boundary crack. When Mk is lower than 0.075, α-Mg grain boundary cracks tend to form. Few cracks are generated at the phase boundary is due to the mild strain partitioning between α-Mg phase and β-Li phase and may also be partly attributed to multiple slip systems in body-centered cubic (BCC)-structured β-Li phase, which can accommodate well with the deformation of adjacent α-Mg phase.

Towards the understanding of fracture resistance of an ultrahigh-strength martensitic press-hardened steel

Identifying the fracture resistance capabilities and gaining a deeper understanding of the controlling damage mechanisms are important to the development of press-hardened steels (PHS) for automotive applications. In this study, the fracture properties of a novel PHS alloyed with Cr and Si (CrSi-PHS) were assessed by using uniaxial tensile and double-edge notched tensile (DENT) tests. Under uniaxial tension, the fracture resistance is characterized by the fracture strain and work of fracture, and the CrSi-PHS presents a desirable compromise with strength when comparing with other grades of advance high-strength steels (AHSS). The large fracture strain is attributed to the high resistance to damage nucleation even with a high density of grain boundaries. Fracture toughness is characterized by the DENT tests. The fracture toughness parameters of CrSi-PHS are lower than that of the commercial PHS 22MnB5 but comparable to the multiphase AHSSs with lower strength levels. The stress triaxiality near the fatigue pre-crack in DENT tests leads to a change of damage mechanism in CrSi-PHS. The crack propagates discontinuously by joining the micro-cracks and subsequently by the ductile fracture of micro-ligaments. The local plasticity at the crack tip region is suggested to contribute significantly to the energy dissipation. The observations demonstrate a strong dependence of the fracture mode and fracture resistance on the loading condition in the ultrahigh-strength martensitic steels.

Composition-dependent transformation-induced plasticity in Co-based complex concentrated alloys

While the mechanically-induced martensitic transformation and transformation-induced plasticity (TRIP) effects have various known benefits, transformation of blocky martensite can also accelerate ductile damage nucleation and growth. Some complex-concentrated alloys (CCAs) with negative stacking-fault energy (SFE) demonstrate a rare faulting plasticity behavior with high strain hardening capability, that sets them apart from conventional low, positive SFE alloys that exhibit the TRIP effect. This study investigates the influence of dilute nitrogen on the TRIP mechanisms in a Co-rich CoCrNi CCA, and reveals, among other findings, that nitrogen interstitials can effectively reduce the extension of stacking faults and deformation-induced phase transformation, resulting in higher strain hardenability at early deformation levels and ductility. Thermodynamic calculations are coupled to various experimental analyses based on atom-probe tomography, scanning transmission electron microscopy, electron backscattered diffraction, electron-channeling contrast imaging, in situ high-energy synchrotron X-ray diffraction, and stress relaxation testing, to explore the origins of the observation. This work provides insights into the future design of CCAs with desirable TRIP, faulting plasticity, and mechanical properties.

Local structural ordering determines the mechanical damage tolerance of amorphous grain boundary complexions

Amorphous grain boundary complexions act as toughening features within a microstructure because they can absorb dislocations more efficiently than traditional grain boundaries. This toughening effect should be a strong function of the local internal structure of the complexion, which has recently been shown to be determined by grain boundary crystallography. To test this hypothesis, molecular dynamics are used here to simulate dislocation absorption and damage nucleation for complexions with different distributions of structural short-range order. The complexion with a more disordered structure away from the dislocation absorption site is actually found to better resist crack nucleation, as damage tolerance requires delocalized deformation and the operation of shear-transformation zones through the complexion thickness. The more damage tolerant complexion accommodates plastic strain efficiently within the entire complexion, providing the key mechanistic insight that local patterning and asymmetry of structural short-range order controls the toughening effect of amorphous complexions.

Nonlocal geometric fracture theory: A nonlocal‐local asymptotically compatible framework for continuous–discontinuous deformation of solid materials

SummaryOne of the fundamental but unsolved problems in fracture mechanics of solid materials is how to describe the continuous and discontinuous deformation of continuum in a unified manner. This paper aims to develop a novel nonlocal geometric fracture theory attempting to address this essential issue. Using the concepts of nonlocal calculus, a new nonlocal equation for the deformation of continuum is obtained by minimizing a nonlocal Lagrangian. This is done to ensure that the proposed nonlocal model can be used to describe the continuous and discontinuous deformation of a continuum in a unified geometric manner, as well as to be asymptotically compatible with the classical continuum theory. Inspired by the phase field fracture theory, a nonlocal geometric crack surface functional is proposed to approximate the Griffith fracture energy in continuum. Note, however, that a distinguished feature of the proposed functional is that it enables strong discontinuities appear in the crack phase fields, which is difficult for the phase field fracture theory. After obtaining the nonlocal fracture energy, a nonlocal elastic energy is phenomenologically decomposed into volumetric and deviatoric parts, and then a system of nonlocal geometric fracture equations is derived to describe the damage nucleation, cracks initiation and propagation, which covers the whole physical process of fracture in solid materials. A staggered discontinuous Galerkin method is developed to reach an accurate and stable numerical solution. Numerical examples demonstrate the proposed theory can well capture the transition from the continuous to discontinuous deformation of the continuum and accurately describe the topological evolution of cracks in a unified framework.

Twinning induced spatial stress gradients: Local versus global stress states in hexagonal close-packed materials

Length scale dependent microstructural heterogeneities serve as effective pathways in engineering materials for providing simultaneous strength-ductility enhancement. In this regard, hexagonal close-packed (hcp) materials that exhibit a combination of slip and multiple twinning modes potentially act as ideal candidates that generate heterogeneous microstructures. However, such an inhomogeneous distribution of crystallographic defects also results in build-up of spatially heterogeneous local stress gradients that can be distinct from globally applied stress state. In particular, stress fields arising at the vicinity of deformation twins and due to their interaction with grain interfaces often act as precursors to damage nucleation in most hcp metals and alloys. Hence, assessment of such local stresses and their overall impact on plasticity becomes necessary in order to understand the relationship between twinning and fracture in hcp materials. The current work utilizes commercially pure titanium (cp-Ti) as a model material to investigate the impact of twinning induced stress gradients on the local mechanical response. By means of correlative multiscale structural characterization and local stress gradient measurements, we establish a definitive relationship between applied stress vis-à-vis local stress on the local plasticity behavior ahead of a {112¯2} compression twin-grain boundary intersection in cp-Ti. Additionally, the role of twin interfacial structure for tension and compression twinning modes are experimentally determined and their corresponding impact on the local stress fields and associated twin migration mechanisms is assessed.

On the damage behaviour in dual-phase DP800 steel deformed in single and combined strain paths

Ductile damage in dual-phase steels deteriorates the mechanical properties, resulting in a lowered crashworthiness and a shorter life-time under cyclic loading. However, most works focus on the observation of damage under simple strain paths, even though work pieces are often subjected to combined strain paths during forming. In this work, we set out to characterise the damage behaviour for a DP800 steel subjected to combinations of tensile and bending loads. To this end, we use an automated approach based on machine learning to quantify damage in high-resolution SEM panoramic images, coupled with finite element modelling to determine the stress state, and high-throughput nanoindentation to determine the strain hardening behaviour. We find a strong connection between loading direction and damage formation in both steps of the forming process. By focussing on different possible combinations of positive and negative triaxiality, we show that the combination of two deformation modes with positive triaxiality leads to a promotion of damage formation. A negative triaxiality applied after a positive triaxiality leads to void closure, reducing the number of damage sites and total void area. Importantly, deformation with negative triaxiality carried out before deformation with positive triaxiality inhibits damage nucleation and growth due to strain hardening.