Rate-dependent Fracture Research Articles

Dynamic failures at the metal-glass interface under impact loading

To investigate dynamic fracture behavior in the metal, three metal spheres (e.g., steel sphere, high purity tungsten sphere, and high purity lead sphere) are accelerated by the gas gun devices to impact glass spheres under the critical speed range (i.e., from 70 m/s to 210 m/s). The velocity interferometer system for any reflector (VISAR) devices are employed to measure the particle velocities at the back surface of glass sphere, and high-speed photographs are utilized to capture the failure process at the metal-glass interface. Due to the asynchronous evolutions of stress fields and strain fields in the violent failure process, the results illustrate quite different failure mechanisms from those by the Split Hopkinson Pressure Bar (SHPB) impacting. Fragmentations of the glass sphere are caused mainly by the radial cracks and the lateral cracks around the metal-glass interface and the edges of the sphere with increasing impact velocity. Dynamic failures in the three metal impactors exhibit different modes, e.g., tensile fracture in the steel impactor, shear fracture in the tungsten impactor, and compressed yielding in the lead impactor. The transferring of strain energy releasing is introduced to describe the failure behavior at the metal-glass interface, and a relaxation-diffusion equation of strain energy releasing is then established based on the experimental results and the numeric results by the discrete element method (DEM). The evolutions of failures at the metal-glass interface are discussed. Further investigation is conducted to describe the dynamic fractures in tungsten impactors and steel impactors based on the dimensional analyses, and the quantitative expressions of these strain rate dependent fracture strains and crack width in the metal impactors are obtained. The results are helpful for the profound understanding of the dynamic fracture in the metal structures and the dynamic fragmentations in the brittle material when subjected to impact loading.

Experimental and numerical investigations on rate-dependent fracture behavior of concrete-rock interface

To ensure the safety and stability of the concrete gravity dams built in the seismic regions, this study investigated the rate-dependent fracture behavior of the concrete-rock interfaces with different roughness degrees. Firstly, direct tensile tests and three-point bending tests were conducted to measure the mechanical and fracture properties of the concrete-rock interface with three roughness degrees, i.e. the 4 × 4 interface, natural interface, and 7 × 7 interface, and under four strain rates, i.e. 10-5/s, 10-4/s, 10-3/s, and 10-2/s. By employing the fictitious crack model and initial fracture toughness-based crack propagation criterion, numerical simulations were conducted to analyze the crack propagation processes of the concrete-rock interfaces under different strain rates. The results indicated that the tensile strength and initial fracture toughness exhibited an obvious increasing tendency with the increase of the strain rates, and they showed a nearly linear relationship with the logarithms of the strain rates. Prediction models were proposed to calculate the tensile strength and initial fracture toughness of the concrete-rock interface under different strain rates. In addition, the initial fracture toughness-based crack propagation criterion was proved to be applicable to analyze the crack propagation processes of the concrete-rock interfaces under both quasi-static and seismic strain rates. It was found that the fully-formed fracture process zone lengths and the corresponding crack length decreased obviously with the increase of the strain rates, indicating that the boundary effect of the concrete became stronger under the higher strain rates, which approached to the fracture behaviors of the large-size specimens.

Temperature- and Rate-Dependent Fracture in Disulfide Vitrimers.

The fracture behaviors of disulfide vitrimers are highly rate-dependent. Our investigation revealed that the temperature-dependent fracture behaviors of disulfide vitrimers cannot be entirely explained by a simple time-temperature superposition model. This Letter explores the impact of the dynamic nature of molecular defects on the temperature- and rate-dependent fracture behaviors of disulfide vitrimers. Considering that the high cross-linking density remains constant during the associated bond exchange reaction, we identify loop defects in the network as the primary dynamic defects. By employing small amplitude oscillatory shear, we measured the loop defect fraction in EPS25 disulfide vitrimers at varied temperatures, revealing an increased presence of loop defects at elevated temperatures. Furthermore, our findings indicate that the temperature-dependent fracture behaviors are attributed to the temperature-dependent number of loop defects in disulfide vitrimers.

Modeling of viscoelastic deformation and rate-dependent fracture damage in rat bone

Bone is a complex hierarchical structural material whose organ-level response is highly influenced by its constitutive behavior at the microstructural level, which can dictate the inelastic nonlinear deformation and fracture within the organ. In the current study, a combined experimental-computational approach was sought to first obtain the local constitutive properties. Later, a multiscale modeling framework utilizing a novel rate-dependent nonlinear viscoelastic cohesive zone (NVCZ) model was used to explore the fracture behavior at the microstructure of the bone and its influence on the global scale (organ-level) response. Toward this end, nanoindentation testing was conducted within the cross-section of a rat femur bone specimen. An inverse optimization process was used to identify the isotropic linear viscoelastic (LVE) properties of cortical bone by integrating the test results with a finite element model simulation of the nanoindentation testing. Model results using different numbers of spring-dashpot units in the generalized Maxwell model showed that four spring-dashpot units are sufficient to capture the LVE behavior, while solely LVE constitutive relation is limited to fully characterize the rat femur. The LVE constitutive properties were then used along with the rate-dependent NVCZ fracture within the representative volume element (RVE), which was two-way coupled to the global scale bone. A parametric study was conducted by varying the fracture properties of the NVCZ model. The model demonstrated the capability and features to represent inelastic deformation and nonlinear fracture that are linked between length scales. This further implies that the inelastic fracture model and the two-way coupled modeling can elucidate the complex multiscale deformation and fracture of bone, while model validation and further advancements with test results remain a follow-up study and are currently in progress.

Fibrin clot fracture under cyclic fatigue and variable rate loading

Fibrin clot is a vital class of fibrous materials, governing the mechanical response of blood clots. Fracture behavior of fibrin clots under complex physiological load is relevant for hemostasis and thrombosis. But how they fracture under cyclic and variable rate loading has not been reported. Here we conduct cyclic fatigue and monotonic variable rate loading tests on fibrin clots to characterize their fracture properties in terms of fatigue threshold and rate-dependent fracture toughness. We demonstrate that the fracture behavior of fibrin clots is sensitive to the amplitude of cyclic load and the loading rate. The cyclic fatigue tests show the fatigue threshold of fibrin clots at 1.66 J/m2, compared to the overall fracture toughness 15.8 J/m2. Furthermore, we rationalize the fatigue threshold using a semi-empirical model parameterized by 3D morphometric quantification to account for the hierarchical molecular structure of fibrin fibers. The variable loading tests reveal rate dependence of the overall fracture toughness of fibrin clots. Our analysis with a viscoelastic fracture model suggests the viscoelastic origin of the rate-dependent fracture toughness. The toughening mechanism of fibrin clots is further compared with biological tissues and hydrogels. This study advances the understanding and modeling of fatigue and fracture of blood clots and would motivate further investigation on the mechanics of fibrous materials. Statement of significanceFibrin clot is a soft fibrous gel, exhibiting nonlinear mechanical responses under complex physiological loads. It is the main load-bearing constituent of blood clots where red blood cells, platelets and other cells are trapped. How the fibrin clot fractures under complex mechanical loads is critical for hemostasis and thrombosis. We study the fracture behavior of fibrin clots under cyclic fatigue and monotonic variable rate loads. We characterize the fatigue-threshold and viscous energy dissipation of fibrin clots. We compare the toughness enhancement of fibrin clots with hydrogels. The findings offer new insights into the fatigue and fracture of blood clots and fibrous materials, which could improve design guidelines for bioengineered materials.

Rate- and temperature-dependent ductile-to-brittle fracture transition: Experimental investigation and phase-field analysis for toffee

The mechanical behaviour of many materials, including polymers or natural materials, significantly depends on the rate of deformation. As a consequence, a rate-dependent ductile-to-brittle fracture transition may be observed. For toffee-like caramel, this effect is particularly pronounced. At room temperature, this confectionery may be extensively deformed at low strain rates, while it can behave highly brittle when the rate of deformation is raised. Likewise, the material behaviour does significantly depend on temperature, and even a slight cooling may cause a significant embrittlement.In this work, a thorough experimental investigation of the rate-dependent deformation and fracture behaviour is presented. In addition, the influence of temperature on the material response is studied. The experimental results form the basis for a phase-field modelling of fracture. In order to derive the governing equations of the model, an incremental variational principle is introduced. By means of the validated model, an analysis of the experimentally observed ductile-to-brittle fracture transition is performed. In particular, the coupling between the highly dissipative deformation behaviour of the bulk material and the rate-dependent fracture resistance is discussed.

High strain rate constitutive and fracture characterization of AA7075-T6 sheet under various stress states

The stress state and strain rate dependent fracture behavior of high strength aluminum sheet, AA7075-T6, is characterized experimentally and numerically. Experiments were performed using shear, hole tension, notch tension, and groove tension specimen geometries at strain rates in the regime 10−2 – 500 s−1. The temperature change on the specimen surface was measured utilizing high speed thermal imaging, while strains were acquired using DIC-based optical measurements. Mild positive rate sensitivity was observed in the flow response for equivalent strains up to approximately 20%, while the flow stress decreased at higher (500 s−1) strain rates as the strain levels increased. An increase in temperature was observed within the gauge region of the specimens during elevated strain rate (500 s−1) tests leading to thermal softening. Positive strain rate sensitivity was observed in the measured axial force response for the hole tension and notch tension specimens. The fracture limits of the AA7075-T6 in the shear, hole tension, and notch specimens decreased between strain rates of 0.01 and 10 s−1, then increased at strain rates between 10 and 500 s−1. A strain rate and temperature dependent Hockett–Sherby (HS-SRT) constitutive model was proposed to capture the dependency of the flow stress on the equivalent plastic strain, strain rate, and temperature. The generalized Drucker-Prager (GDP) fracture model was extended to capture the effect of strain rate on fracture initiation. Numerical simulations of the coupon experiments were then performed to extract the local stress and strain states to calibrate the GDP fracture model across the range of strains considered.

Rate-dependent fracture behavior of gelatin-based hydrogels

Rate-dependent fracture behavior of gelatin-based hydrogels

Mechanism of nanoscale helium bubbles influencing dynamic tensile response of polycrystalline copper

This work investigates the mechanism of nanoscale helium (He) bubbles influencing the dynamic tensile response of quasi two-dimensional (2D) polycrystalline copper (Cu), based on molecular dynamics simulations. The dynamic fracture behaviors are explored under two different loading conditions (uniaxial tensile loading and shock loading). For uniaxial tensile loading, it's found the effect of He bubble on the tensile strength gets weaker with the increasing strain rate. A strain rate-dependent fracture mechanism that transforms from the growth and coalescence of He bubbles to the cleavage fracture of grain boundaries (GBs) as the strain rate increases is investigated. Under shock loading, the effect of He bubble on reducing the spall strength of polycrystalline Cu is more significant at lower impact velocities and will disappear as the impact velocity increases higher. The mechanism of spall damage is investigated by comparing the effect of He bubbles, voids and GBs under different impact velocities. Additionally, the dynamic response under the above two loading conditions is compared. The results indicate that the effect of He bubble distribution on the strength is more significant under shock loading than uniaxial tensile loading.

Factors in deformation capacity loss of bolts under singular and consecutive impacts

For structures subjected to extreme loading, such as a blast or impact, the plastic deformation of structural connections is vital to life safety. Despite its importance, a loss of deformation capacity in connections via fracture of bolts has been repeatedly noted experimentally and in situ. To further investigate the dynamic fracture of bolts, this work subjects A325 structural bolts in single shear to impulsive loads using a high-speed hydraulic actuator. This is the first study to report strength and deformation performance for structural bolts fractured via singular and consecutive impacts. Further, this work is the first investigation into the root cause of the deformation capacity loss that has historically coincided with shear bolt fracture. Previous split Hopkinson pressure bar experimentation suggests that rate-induced changes in strain hardening contribute to, but do not fully explain, the loss of deformation capacity in high-strength bolts. Further investigation with scanning electron microscopy suggests that loss of deformation capacity is also due to a rate-induced change in failure mechanism, adiabatic shear banding. These findings impact our understanding of connections that fail via dynamic bolt fracture – behavior changes on the macroscale are the result of underlying rate-dependent fracture mechanisms.

Experimental and computational models for simulating the oral breakdown of food due to the interaction with molar teeth during the first bite

The first bite involves the structural breakdown of foods due to the interaction with teeth and is a crucial process in oral processing. Although in vitro experiments are useful in predicting the oral response of food, they do not facilitate a mechanistic understanding of the relationship between the intrinsic food mechanical properties and the food behaviour in the oral cavity. Computer simulations, on the other hand, allow for such links to be established, offering a promising design alternative that will reduce the need for time consuming and costly in vivo and in vitro trials. Developing virtual models of ductile fracture in soft materials, such as food, with random and non-predefined crack morphology imposes many challenges. One of the most important is to derive results that do not depend on numerical parameters, such as Finite Element (FE) mesh density, but only physical constants obtained through independent standard mechanical tests, such as fracture strain and/or critical energy release rate. We demonstrate here that this challenge can be overcome if a non-local damage approach is used within the FE framework. We develop a first bite FE modelling methodology that provides mesh independent results which are also in agreement with physical first bite experiments performed on chocolate. The model accounts for key features found in chocolate and a wide range of compliant media, such as rate dependent plasticity and pressure dependent fracture initiation strain. As a result, our computational methodology can prove valuable in studying food structure-function relationships that are essential in product development.

A coupled thermo-mechanical cohesive zone model for strain rate-dependent fracture of hat-shaped specimens under impact

A coupled thermo-mechanical cohesive zone model for strain rate-dependent materials is proposed to illustrate the shear failure in the hat-shaped specimens made of U75V rail steel at various impact loads and temperatures.The cohesive energy and the maximum cohesive stress in the proposed cohesive zone model depend on strain rates and temperatures. The coefficients in the functions of cohesive energy, maximum cohesive stress, and the cohesive law are obtained through a combination of experimental and simulation data. The experimental strain waveforms are obtained by a split Hopkinson pressure bar system and the cohesive zone model is implemented using ABAQUS finite element software with the assistance of user subroutines.The findings substantiate the efficacy of the proposed cohesive zone model in accurately predicting the shear failure of hat-shaped specimens under high-speed impacts, as evidenced by the notable concurrence between experimental and computational outcomes within an acceptable margin of error. Notably, the cohesive energy and maximum cohesive stress in the model demonstrate a dual dependency on strain rates and thermal conditions, emphasizing the significance of considering both thermal and mechanical effects when simulating shear failure in materials experiencing high temperatures and high strain rates.

Phase-field modelling and analysis of rate-dependent fracture phenomena at finite deformation

AbstractFracture of materials with rate-dependent mechanical behaviour, e.g. polymers, is a highly complex process. For an adequate modelling, the coupling between rate-dependent stiffness, dissipative mechanisms present in the bulk material and crack driving force has to be accounted for in an appropriate manner. In addition, the resistance against crack propagation can depend on rate of deformation. In this contribution, an energetic phase-field model of rate-dependent fracture at finite deformation is presented. For the deformation of the bulk material, a formulation of finite viscoelasticity is adopted with strain energy densities of Ogden type assumed. The unified formulation allows to study different expressions for the fracture driving force. Furthermore, a possibly rate-dependent toughness is incorporated. The model is calibrated using experimental results from the literature for an elastomer and predictions are qualitatively and quantitatively validated against experimental data. Predictive capabilities of the model are studied for monotonic loads as well as creep fracture. Symmetrical and asymmetrical crack patterns are discussed and the influence of a dissipative fracture driving force contribution is analysed. It is shown that, different from ductile fracture of metals, such a driving force is not required for an adequate simulation of experimentally observable crack paths and is not favourable for the description of failure in viscoelastic rubbery polymers. Furthermore, the influence of a rate-dependent toughness is discussed by means of a numerical study. From a phenomenological point of view, it is demonstrated that rate-dependency of resistance against crack propagation can be an essential ingredient for the model when specific effects such as rate-dependent brittle-to-ductile transitions shall be described.

A nonlinear and rate-dependent fracture phase field framework for multiple cracking of polymer

Designing durable polymer-based materials and structures requires understanding how the physical processes and failure mechanisms associated with moisture intrusion and loading rate combine to produce the complex damage modes observed in their applications. While numerous experiments have assisted us in gaining general insight into the above issues, in-situ characterization is still lacking, and rational prediction on the failure procedure of polymer in the moisture–mechanical​ coupling environment remains challenging. Here we present a thermodynamically consistent theoretical framework and its computational implementation to reveal how the dependence of epoxy’s mechanical behavior on rate- and moisture dictates the initiation and evolution of highly localized deformation zones and cracks. A multi-physical hydrothermal-viscoelastic–viscoplastic-damage model is first proposed to fully couple the effects of strain rate, moisture degradation, strain softening, and adiabatic heating of the bulk epoxy in a highly humid environment. The constitutive models are augmented by a phase field that enables spontaneous tracing of the nucleation and growth of cracks under a wide range of strain rates (from 4.60 × 10−5/s to 3.80 × 103/s). The theoretical model is implemented into an efficient computational procedure that is used to calculate illustrative examples to demonstrate the influence of the intimate coupling between the multi-physical phenomena. The results highlight significant mechanisms underlying the coupled damage process, including: heat accumulation along the crack propagation path; identification of the energies associated with moisture-induced toughening; prediction of crack deflection in the presence of moisture absorption; and illustration that a portion of the plastic work plays a dominant role in the nucleation of cracks at a wide scale of strain rates.

A statistical model of the rate-dependent fracture behavior of dental polymer-based biomaterials.

An insight into the fracture behavior of dental polymer-based biomaterials is important to reduce safety hazards for patients. The crack-driven fracture process of polymers is largely stochastic and often dependent on the loading rate. Therefore, in this study, a statistical model was developed based on three-point bending tests on dental polymethyl methacrylate at different loading rates. The fracture strains were investigated (two-parameter Weibull distribution (2PW)) and the rate-dependency of the 2PW parameters were examined (Cramér-von Mises test (CvM)), arriving at the conclusion that there could be a limiting distribution for both quasi-static and dynamic failure. Based on these findings, a phenomenological model based on exponential functions was developed, which would further facilitate the determination of the failure probability of the material at a certain strain with a given strain rate. The model can be integrated into finite element solvers to consider the stochastic fracture behavior in simulations.

Effect of loading rate and material viscosity on fracture energy dissipation

The numerical study in this paper highlights the relationship between viscoelasticity and fracture energy dissipation in engineering materials. Literature available on three-point bending experiments on concrete and limestone at different loading rates motivated a hypothesis that the material viscoelasticity causes the loading rate-dependent fracture energy dissipation. To test this hypothesis, we analyze a simple mechanical unit consisting of two rigid bars held together by multiple elemental units under varying loading rates. Each elemental unit has a material softening element (simulating fracture energy dissipation) and a viscoelastic element (Kelvin element). The energy dissipated by the softening elements and the size of damage (number of softened elements) in the mechanical unit at peak load increase with the loading rate. This result supports our hypothesis that material viscosity causes the fracture energy dissipation and the damage zone's size to be dependent on the loading rate.

Rate-dependent fracture of hydrogels due to water migration

When a hydrogel deforms, the water molecules inside the hydrogel move together with the polymer network. At a particular time scale and length scale, the water migration within the hydrogel as well as the water exchange with the environment can greatly affect the deformation of the hydrogel. In this work, we study the rate-dependent fracture of hydrogels due to water migration both experimentally and theoretically. We build an experimental setup that can apply mechanical loads to hydrogel samples immersed in a liquid environment, water or oil. We apply monotonic load to hydrogel samples under different loading rates and find that the fracture stretch of hydrogel is highly dependent on the loading rate when the hydrogel is immersed in water, and is almost independent of the loading rate when the hydrogel is immersed in oil. We also apply step load to hydrogel samples and find that the hydrogel immersed in water is more susceptible to delayed fracture than that immersed in oil. We adopt the large deformation theory incorporating water migration developed by Hong et al. (2008) and use finite element software to calculate the deformation and fracture of hydrogels under the two types of environmental conditions. The numerical calculations show that at the time scale and length scale used in the experiment, the water migration satisfies the small-scale swelling condition of fracture. When the hydrogel is immersed in water, the water molecules can exchange with the environment under different loading rates. When the hydrogel is immersed in oil, the water molecules can hardly move in or out of the hydrogel. The theoretical predictions explain the experimental results.

A developed 3D peridynamic method incorporating non-conservative force for brittle materials

A 3D peridynamic method involving the work done by the non-conservative force is developed, whose theoretical framework comprises two parts: the viscoelastic motion equation of material points and the rate-dependent fracture criterion of the bond. For the description of motion, a viscoelastic interaction model between material points is proposed based on the understanding deformation mechanism of concrete. Further, the viscoelastic motion equation is theorized by applying Hamilton's principle which considers the energy dissipation, as a result, the viscoelastic deformation of brittle material can be captured. The elastic and viscous parameters are calibrated by the energy density equivalence between the developed 3D peridynamic method and the classical continuum mechanics under the same deformation condition. For the control of strength and cracking, the dynamic uniaxial S strength criterion is introduced into the fracture criterion of the bond so that the rate-dependent behavior of strength and cracking failure can be reflected. The function and superiority of the developed 3D peridynamic method are discussed via numerical experiments. It is found that the developed peridynamic method can reasonably reflect the influence of loading rate on the deformation, strength, and cracking of brittle material.

Rate dependent fracture behavior of highly cross-linked epoxy resin

The fracture behavior of highly cross-linked epoxy resin under plane strain conditions for crack tip strain rates spanning over four orders of magnitude (10-4 −10-1 s−1) has been examined. The plane strain fracture toughness initially decreases with increasing crack tip strain rate (∊̇tip) and saturates at ∼ 0.8 MPa-m−0.5 after ∊̇tip ∼ 0.02 s−1 is attained. For all the fracture specimens, a fracture process zone (FPZ) forms ahead of the sharp pre-crack prior to catastrophic failure due to the intensified stresses ahead of the crack tip. This FPZ region consists of crazes that govern the micro mechanism of fracture and this was explicitly proved using in-situ testing in a scanning electron microscope. For low strain rates, crazing in the FPZ is expected to be dominated by chain disentanglements, with craze openings more than 200 nm, whereas, chain-scission is expected to dominate at higher strain rates, with lower craze openings of ∼ 150 nm.

Loading Mode and Lateral Confinement Dependent Dynamic Fracture of a Glass Ceramic Macor

AbstractA systematic comparison of the tensile and compressive response of glass ceramic Macor, with zero porosity and low density, is carried out by using flattened Brazilian disk and cylindrical specimen from quasi-static to dynamic loading conditions. The experiments were performed on a screw driven Zwick machine and an in-house built split Hopkinson bar synchronized with a high speed photographic system. Likewise, the loading rate dependent fracture toughness is also investigated by using a notched semi-circular Brazilian disk. A digital image correlation technique is adopted to assist in the monitoring of strain field, crack initiation and propagation under dynamic loading conditions. Both tensile and compressive strength show loading rate dependencies, however, the static and dynamic tensile strengths are only 20% of the compressive strengths without confinement and less than 10% of the confined compressive strength. The microstructural characterization reveals the fracture mechanisms in unconfined Macor are predominantly transgranular with mica platelets and cleavage planes, which are influenced by the loading mode and loading rate. However, the Macor with confinement shows ductile fracture micrographs with a shear localization zone consisting of fine particles. With the use of Macor ceramic as a model material, the paper presents an economical approach to investigate the loading mode and pressure dependent failure of ceramic materials. This will support the characterization of dynamic properties of current and future developed advanced ceramics for demanding applications in the aero engine.