Quasi-static Material Research Articles

Modified cure cycles for increased fatigue performance of fiber metal laminates

Modified (MOD) cure cycles that deviate from the manufacturer’s recommended cure profile can reduce the inherent thermally induced residual stresses (TRS) in fiber metal laminates (FML). Literature shows that MOD cycles do not adversely affect the material properties but enhance the quasi-static material strength. However, the literature does not comprehensively discuss the impact of MOD cycles on material performance during cyclic fatigue loading. This paper, therefore, investigates how MOD cycles influence the fatigue characteristics of different FML layups made of carbon fiber-reinforced polymer (CFRP) and steel. The experimental results confirm that the quasi-static material strength and the modulus of the FML are increased when using MOD cure cycles. The evaluation of fatigue tests with digital image correlation, thermography, and electrical resistance measurements of notched specimens shows that a reduction of TRS delays damage initiation in the metal facesheets and decreases the crack growth rate until facesheet failure. The results further show that layup-dependent parameters, the maximum stress in the metal sheets, and metal sheet thickness significantly govern the evolution of fatigue damage. In summary, modified cure cycles are an efficient tool to enhance the quasi-static and fatigue performance of CFRP-steel hybrid laminates.

Enabling magnetic pulse welding for dissimilar tubular arrester cable joints

Climate change exacerbates the need for resource-efficient and cost-effective production processes across manifold industries, including the field of electrical connections. This specific field is characterized by a conflict of objectives, i.e., weight reductions while maintaining joint strength and electrical conductivity. From a material point of view, the use of aluminum as a conductor material is suitable for this application, as it is lighter than copper, a classical conductor material. Electrical conductors are often used in the form of flexible cables, so-called stranded wires. This type of conductor as well as the fact that the sole use of aluminum in electrical systems is not feasible, e.g., because the predetermined connection terminals of power electronic components are made of copper, creates a substantial demand for dissimilar aluminum-copper cable arrester joints. However, traditional fusion-based welding processes have proved incapable of reliably producing these dissimilar aluminum-copper joints because of thermophysical effects and chemical incompatibilities, the latter eventually leading to the formation of intermetallic phases. These phases adversely affect the quality of the joint in terms of both mechanical and electrical performance. Yet, magnetic pulse welding, a pressure welding process, is ideally suited for producing dissimilar metal joints on the basis of a low energy input during the welding process. Consequently, the formation of intermetallic phases is restrained. However, magnetic pulse welding has not been sufficiently investigated for the reliable contacting of stranded cables to tubular arresters. As a result, this paper focuses on the fabrication of tubular stranded cable arrester joints using magnetic pulse welding. To shed light on possible material combinations, aluminum-to-aluminum and copper-to-copper joints as well as their dissimilar counterparts are welded. Subsequently, the joints are characterized with regard to their microstructure and quasi-static material strength. Electrical characterization comprises the four-wire Kelvin measurement method to evaluate the resistance of the electrical joints. The results demonstrate that magnetic pulse welding is ideally suited to join the aforementioned material combination and joint configuration due to its process characteristics eventually leading to material continuity. As a result, the stranded wires are welded to the tubular arresters rather than crimped. Consequently, a comparative analysis of the joint properties with those of the joining partners shows that the measured electrical resistances and mechanical tensile forces may be considered very good.

Collisions between Drones and Rotorcraft: Modeling of the Crash Response of Battery Packs

Drones operating in an urban environment pose a potential collision threat to rotorcraft. In this paper, the battery pack of the DJI MAVIC 2 ZOOM is analyzed since the battery is considered to be the greatest threat due to its high weight and stiffness. Following a pyramid-type building block approach, a high-fidelity model simulation was developed for LSDYNA based on a wide range of experiments, ranging from quasi-static material tests to quasi-static component tests up to high-velocity impact experiments. The high-fidelity model allows the prediction of damage in potential collision scenarios between a high-speed rotorcraft and the battery pack of the drone. For the particular impact configuration analyzed within this paper, the drone battery does not cause catastrophic failure of the windshield of the rotorcraft.

Numerical Modeling of Pumping-Induced Earth Fissures Using Coupled Quasi-Static Material Point Method

Pumping-induced earth fissuring is a typical fluid–solid coupling problem involving fracture evolution. Despite recent advances in the numerical modeling of earth fissures, a holistic approach capable of predicting their evolution and understanding their behavior from fracture mechanisms is absent. This paper presents a coupled numerical method based on the framework of the material point method (MPM) and fracture mechanics for the process-oriented simulation of pumping-induced tensile earth fissures. In this method, fissure behavior is driven by the real-time stress field affected by soil consolidation. After an earth fissure initiates in the region of maximum tensile stress, it propagates in the direction of the maximum circumferential stress around the fissure tip. The great scale difference between a fissure tip and the entire model is addressed with an adaptive refinement strategy. Through the simulation of a physical model experiment reproducing pumping-induced earth fissures with the presence of a bedrock ridge, the complete fissuring process, including initiation, propagation, and arrest, is presented. The simulated fracture time (24 h after drainage), location (directly above the bedrock ridge), final length (165 mm), and morphology evolution (from straight to zigzag) of the main fissure basically were in agreement with the experimental results. The stress intensity factors (SIFs) around fissure tips, which are important fracture parameters that have not been discussed in existing earth fissure analyses, also are captured during the fissure growth. The proposed method quantifies the inhibition of geostatic stress fields in earth fissure development and correlate fissure morphology with the stress field at a fissure tip.

Constitutive strength model for spot joints of thin-walled energy-absorbing elements

The goal of this paper was to determine the strength criterion that causes the failure of point-to-point joints of thin-walled profiles under impact load, as well as to determine the strength parameters that guarantee joint continuity during dynamic folding of crash boxes. For this purpose, extensive quasi-static and dynamic materials tests were conducted for the five most popular steel grades used in the automotive industry: DP600, DP800, DP1000, HSLA and DC01. The strength of the spot joints was investigated in acomplex load state using the original instrumentation. This allowed authors to build and validate mathematical models of the load-bearing capacity of point-to-point joints and to conduct simple and efficient numerical simulations of these elements without the need to account for their geometry. Following the validation of mathematical models and load-bearing models of the joints, extensive experiments of quasi-static and dynamic crushing of thin-walled energy-absorbing top-hat (TH) structures were conducted. The data collected made it possible to calibrate the FEM model correctly and conduct numerical simulations of the dynamic crushing of energy-absorbing structures. As a result, the minimum shear strength (Fs) and cross-tension strength (Fn) of the joints were determined as a function of the sheet thickness and the parameters of Re and Rm. The creation of any spot joint enabling the simultaneous carrying of forces Fs and Fn ensures the preservation of joint continuity throughout the entire crushing process and makes it possible for manufacturers to select the type of spot joint based only on its strength.

Development and Validation of a Dynamic Abdominal Pressure Twin Sensor Finite Element Model

<div>Some anthropomorphic test devices (ATDs) currently being developed are equipped with abdominal pressure twin sensors (APTS) for the assessment of abdominal injuries and as an indicator of the occurrence of the submarining of an occupant during a crash event. The APTS is comprised of a fluid-filled polyurethane elastomeric bladder which is sealed by an aluminum cap with an implanted pressure transducer. It is integrated into ATD abdomens, and fluid pressure is increased due to the abdomen/bladder compression due to interactions with the seatbelt or other structures. In this article, a nonlinear dynamic finite element (FE) model is constructed of an APTS using LS-PrePost and converted to the LS-Dyna solver input format. The polyurethane bladder and the internal fluid are represented with viscoelastic and isotropic hypoelastic material models, respectively. The aluminum cap was considered a rigid part since it is significantly stiffer than the bladder and the fluid. To characterize the APTS, dynamic compression tests were conducted on a servo-hydraulic load frame under displacement control and held at the peak compression to allow for stress relaxation prior to slowly releasing the compression amount. The initial peak pressures and loads were 15–17% above the level observed at a 10-second hold period with 50% of the decay occurring within 300 ms. The material properties are identified using an inverse method that minimizes the difference between measured and predicted load and pressure time histories. Further, the bio-fidelity static specifications of the APTS manufacturer are used as a basis to identify the quasi-static material parameters. This approach resulted in a reasonable match between physical test data and model-simulated data for dynamic compressions of 10 mm and 15 mm (~50% compression). Additional compression tests are conducted at two compression levels (5 and 10 mm) and at four load offset configurations for use in the model validation. The FE model was used to predict peak pressure responses within approximately 10% error at full-load capacity and achieved CORA ratings >0.99 for the pressure time history. The proposed inverse method is expected to be generally applicable to the component characterization of other models and sizes of APT sensors.</div>

Simulation and dimensional analysis of instrumented dynamic spherical indentation of ductile metals

Finite element (FE) modeling of instrumented dynamic indentation experiments in a miniature Kolsky bar is undertaken. Geometry, including an output bar with machined spherical indenter tip, and velocity history boundary conditions are extracted directly from experimental diagnostics. The test material (i.e., substrate) is polycrystalline aluminum alloy Al 6061-T6. The constitutive model used in simulations accounts for isotropic elasticity and isotropic plasticity with strain hardening, strain-rate hardening, and thermal softening under adiabatic conditions. The FE model, with representative material parameters culled from the literature, accurately reproduces the curvature of the experimental load versus depth data for three different experimental indentation velocity histories. A framework for dimensional analysis of instrumented dynamic spherical indentation is set forth, improving upon prior work. Parametric FE simulations reveal sensitivity, or lack thereof, of the predicted response to variations in the proposed independent dimensionless variables encompassing material properties. For the indenter size, maximum depth, and maximum strain rate imposed experimentally on the order of 103/s, force-depth predictions are nearly unaffected by realistic variations in mass density, melting temperature, and thermal softening parameters when the sample is initially at room temperature. Predictions are affected by elastic constants (the elastic modulus and to a lesser extent, Poisson’s ratio), initial yield strength, two strain hardening parameters, and strain rate sensitivity. Predictions are also notably affected by initial temperature, with thermal softening prominent at high enough initial temperature or much higher loading rates. Based on the dimensional analysis, static indentation and elevated temperature indentation experiments are proposed for extraction of quasi-static and thermal material properties from previously uncharacterized metals, and dynamic indentation is proposed for extraction of rate sensitivity that cannot be obtained from static tests. Rate sensitivity obtained in this way from the novel instrumented dynamic spherical indentation experiments and FE simulations produces a parameterized stress–strain response for Al 6061-T6 reasonably validated by external studies for strain rates up to the order of 103/s.

Low-Cycle Fatigue Behavior of Hot V-Bent Structural Components Made of AZ31B Wrought Magnesium Alloy

Recent studies have shown the change of microstructure during hot-bending in uniaxial specimens made of AZ31B alloy. They also investigated the influence of the changed microstructure on the quasi-static and cyclic material behavior under uniaxial stress states. However, studies on the fatigue behavior of hot-bent structural components in which a multiaxial inhomogeneous stress state occurs are still lacking. For this purpose, a novel hot-bent V-shaped specimen was developed, of which three different variants, each with a different bending radius, were fabricated and investigated. Microstructural analyses reveal that band-like accumulations of twinned grains are already formed in the compressively stressed area of the specimen during the bending process. Force-controlled low-cycle fatigue tests were performed to investigate the twinning evolution after cyclic loading. Subsequent microstructure analyses show that bands of twinned grains are no longer visible but also that the occurrence of twins is evenly distributed. Due to the specimen shape, the specimens are subjected to a multiaxial stress state. During LCF tests, the strain was measured using 3D digital image correlation and fatigue life was modeled successfully with the application of the concept of highly strained volume.

Crack growth modelling in cementitious composites using XFEM

The article focuses on modelling origin damage to heterogeneous materials, especially to the issue of modelling the formation and propagation of cracks in fibre cementitious composites, which leads to total degradation of any structure. This paper studies mathematical models based on the modification of the stress distribution and deformation calculation ahead the crack tip, using programming implementation of appropriate support procedures in Matlab language modifying the standard procedure of the extended finite element method (XFEM) for quasi-static material response. The technique of stress and strain calculation in the area of damage enables simplified and possibly more realistic estimates of the respective fields in the case of modelling the influence of short fibres realizing the reinforcement of construction materials.

Experimental and numerical investigations on the micro-damage behaviour of glass fibre-reinforced plastics

The formation and influence of micro-damage in glass fibre-reinforced plastics (GFRP) is carried out by numerical and experimental investigations. A quasi-static material characterisation is performed and the stiffness and strength of unidirectional, undamaged material in longitudinal and transverse direction as well as in the 23-plane are determined. Since the desired micro-damage could not be generated in unidirectional laminates due to abrupt failure, a [0∘/90∘]s layup has been identified to be most suitable to generate micro-damage in a reproducible way in the 90° layers, which is done using a tension–tension fatigue test program. During these experiments, micro-damage is detected optically and by means of ultrasonic birefringence, where the latter method shows a reduction in shear modulus due to fibre–matrix debonding prior to final inter-fibre failure. The shear modulus degradation is indirectly measured by the change in the velocity of sound. Since this method is limited to measurements in the 13- and 23-plane, all experiments are accompanied with microstructural simulations with detailed statistical volume elements (SVE), to study the influence of micro-damage under various loading conditions and directions. For loading in fibre direction, no influence on the mechanical properties is observed for the investigated fibre–matrix debonding. However, this is different for transverse loading, where a transverse shear stiffness loss of around 8% results in a decrease of transversal stiffness of around 18%, if the load direction is perpendicular to the damage plane. A similar behaviour is observed for the strength, which is reduced by a factor of 2 for the same configuration.

High-velocity impact behaviour of curved GFRP composites for rail vehicles: Experimental and numerical study

This study aims to explore the projectile impact behaviour of curved glass fibre reinforced plastics (GFRP) composites for rail vehicles through experimental and numerical methods. Quasi-static material tests were firstly carried out to obtain the tensile, compression, shear and bending properties. Then, high-velocity impact tests under different velocities were conducted for curved GFRP plates, which were cut from hood covers of a rail vehicle. The residual velocity of the projectile, the failure modes and the energy absorption of the composite targets were analysed. The classical Lambert-Jonas equation was used to predict the critical perforation velocity, which was also verified by the following finite element (FE) simulation in LS-DYNA. Based on the validated FE model, the effects of the impact velocity (65.14–152.22 m/s), target thickness (2 mm–8 mm) and impactor shape (flat, blunt, hemisphere and sphere) on the high-velocity impact performance of the target were studied. The results showed that the predicted critical perforation velocity of the curved GFRP plate with thickness of 6 mm was about 101.98 m/s in this study, and only local damages were observed near the trajectory. Increasing the thickness of the GFRP plate can improve its anti-penetration capability, however, the 4-mm plate possesses the highest specific energy absorption among the thickness of 2 mm–8 mm. Compared to the sharp impactors, the flat impactor resulted in the highest peak force of 260.39 kN and the maximum specific energy absorption of 502.65 J in the curved GFRP plates with thickness of 6 mm, due to the shear failure mechanism and the formation of embolism.

The dynamic material properties of stabilised rammed earth materials using cement and calcium carbonate residue

The use of rammed earth (RE) as a construction material has recently received renewed interest due to its sustainability characteristics and potential for low-cost construction. Modern RE includes the addition of a binder to increase its performance. The mechanical performance of stabilised RE particularly the dynamic material properties is still not well understood. During the design life, a structure could experience dynamic loading. It is necessary to properly understand the dynamic properties of stabilised RE for safe applications. In this study, the quasi-static and dynamic material properties of cement and calcium carbonate residue (CCR) stabilised RE are experimentally investigated. The failure of the stabilised RE under different loading rates is investigated. Dynamic increase effect on cement and CCR stabilised RE are studied. The unconfined uniaxial compressive strength (UCS), Young’s modulus of the two types of stabilised RE at different strain rates are quantified. Empirical formulae of dynamic increase factor are derived for engineering application.

Discussion on the suitability of dynamic constitutive models for prediction of geopolymer concrete structural responses under blast and impact loading

Compared to ordinary Portland cement-based concrete (OPC), geopolymer concrete (GPC) is an environmental-friendly construction material because it is mixed by replacing Portland cement with industry wastes such as fly ash. Despite intensive researches in the last two decades, application of geopolymer concrete in construction is still rather limited. One of the reasons is the quasi-static and dynamic material properties of geopolymer concrete, which are different from those of ordinary Portland-cement concrete, are not well defined yet, and the available design guides for geopolymer concrete structures are very limited. The existing design guides and dynamic constitutive models for OPC cannot be directly employed in design analysis and numerical modelling of GPC structures subjected to blast and impact loads. This paper first summaries the available dynamic material testing data on GPC, compares them with the widely used dynamic constitutive models for OPC, and discusses the suitability of those models for modelling GPC structures. Then, based on the available GPC material testing data, new material constants for strength model, equation of state and dynamic increase factors are derived for GPC. Finally numerical modellings are carried out using these material models with modifications for GPC material to examine their accuracies in simulating the dynamic responses and damages of structural components made of GPC subjected to blast and impact loads.

Numerical Brazilian disk testing of multiscale porous Ultra-High Temperature Ceramics

Recent developments in Ultra-High Temperature Ceramics (UHTC) processing have allowed for the introduction of significant amounts of porosity into these materials. These developments have widened the scope for how UHTCs can be integrated into hypersonic vehicles. Functional grading of porosity allows density and thermal conductivity to be spatially tailored to minimize weight penalty while maintaining thermal shielding and resilience to thermal shock. However, added porosity also results in decreased stiffness and strength. These relationships must be quantified in order to enable porous UHTC component design. In this work, a multiscale computational model using a quasi-static Material Point Method (MPM) implementation is used to quantify the mechanical response of porous UHTCs subject to Brazilian disk testing. The as-implemented MPM algorithm can readily handle large deformations, self-contact and damage. Microscale simulations corresponding to a range of strain states are simulated to calibrate an effective macroscale damage model for use in the macroscale Brazilian disk test simulations. A variety of mesoscale property distributions are considered and used in an initial effort to validate the multiscale modeling approach developed herein, with results closely matching experimental findings after model calibration at the mesoscale.

Impact of ultra-fast (3 s) light-cure on cell toxicity and viscoelastic behavior in a dental resin-based composite with RAFT-mediated polymerization

ObjectiveThe aim of the study was to determine the effects of ultra-fast (3 s) light-curing on the viscoelastic behaviour at clinically relevant frequencies, and cell toxicity, in a resin-based composite (RBC) with reversible addition-fragmentation-chain transfer (RAFT) mediated polymerization. MethodsThree different protocols were used to cure cylindrical samples (height = 4 mm, ϴ = 5 mm), including ultra-fast (3s) cure with high radiant emittance, 10 s and 20 s cure with moderate radiant emittance. The properties of the light curing device were evaluated in all curing protocols by spectrophotometry up to an exposure distance of 10 mm. The light transmission through the samples was determined in real-time with the same spectrophotometer. Absorbance was calculated as a function of wavelength. The quasi-static (indentation hardness/HIT, indentation modulus/EIT) and viscoelastic (storage modulus/E′, loss modulus/E″, loss factor/tan δ) material behavior was determined in an instrumented indentation test with a DMA (Dynamic Mechanical Analysis) module for 10 frequencies (0.5–5 Hz) by profiling the center of the samples in 330 μm steps from top to bottom. Cellular toxicity on human gingival fibroblast (HGF-1) was assessed using a WST-1 colorimetric assay after incubation time of up to 3 months. One and multiple-way analysis of variance (ANOVA) with Tukey honestly significant difference (HSD) post-hoc tests (α = 0.05) were applied. ResultsThe irradiance transmitted through a 4 mm high sample was less than 7% of the incident irradiance, and the absorbance was similar for all curing protocols, showing a decrease with wavelength. Similar quasi-static and viscoelastic parameters were observed regardless of the curing protocol. HIT increased slightly and EIT, E′, E″ and tan δ decreased with frequency. Occasionally, slightly higher confidence intervals were observed for the ultra-fast curing group, which were related to a potential accumulation of stress. The curing protocol had no effect on cell viability (p = 0.326) but the eluate age (p < 0.001, ηP2 = 0.879) did. None of the groups showed cell toxicity at any point in time with respect to the corresponding negative control. ConclusionsThe ultra-fast curing with high irradiance induced no cell toxicity and an equivalent viscoelastic behavior as with conventional curing protocols in a RAFT-modified RBC.

Investigating the mechanical behavior of multiscale porous ultra-high temperature ceramics using a quasi-static material point method

Ultra-high temperature ceramics (UHTCs) are a class of materials that maintain their structural integrity at high temperatures, e.g. 2000 °C. They have been limited in their aerospace applications because of their relatively high density and the difficulty involved in forming them into complex shapes, like leading edges and inlets. Recent advanced processing techniques have made significant headway in addressing these challenges, where the introduction of multiscale porosity has resulted in lightweight UHTCs and a more tailored thermal conductivity response. The effect of porosity on the properties of UHTCs must be characterized to enable design, but doing so experimentally can be costly, especially when attempting to mimic hypersonic flight conditions. As such, this paper seeks to computationally characterize and understand the effective mechanical properties of porous UHTCs, specifically titanium diboride, and validate those results against experimental results so as to build confidence in the model. An implicit quasi-static variant of the Material Point Method (MPM) is developed, whose capabilities include intrinsic treatment of large deformations and contact which are needed to capture the post-elastic behavior of simulated porous UHTC microstructures. It is found that the MPM can approximately obtain the elastic properties of porous UHTCs without calibration, and that the post-elastic results are found to be qualitatively consistent with experimental results. With calibrated input properties, significantly improved agreement is obtained.

Effects of water saturation and low temperature coupling on the mechanical behavior of carbon and E-Glass epoxy laminates

An experimentally based study has been conducted to quantify the effects of coupled water saturation and low temperatures on the quasi-static and dynamic mechanical behavior of E-Glass and Carbon Epoxy laminates. The relative performance of the materials as a function of water saturation and decreasing temperature was characterized through detailed experiments, specifically in-plane (tensile/compressive) and shear material properties, static and dynamic Mode-I fracture, and impact/flexure after impact strength. In the investigation temperatures from Room Temperature (20 °C) down to arctic seawater and extreme ocean depth conditions (−2 °C) were evaluated. The materials utilized in the study, Carbon/Epoxy and E-glass/Epoxy, are chosen due to their primary interest to the underwater vehicle and marine industry communities. The results of the quasi-static and dynamic material experiments show that all properties are affected by both water saturation and decreasing temperature, although the trends are specific to the property under consideration.

Numerical investigation of the failure mechanism of cubic concrete specimens in SHPB tests

Cylindrical specimens are commonly used in Split Hopkinson pressure bar (SHPB) tests to study the uniaxial dynamic properties of concrete-like materials. In recent years, true tri-axial SHPB equipment has also been developed or is under development to investigate the material dynamic properties under tri-axial impact loads. For such tests, cubic specimens are needed. It is well understood that static material strength obtained from cylinder and cube specimens are different. Conversion factors are obtained and adopted in some guidelines to convert the material strength obtained from the two types of specimens. Previous uniaxial impact tests have also demonstrated that the failure mode and the strain rate effect of cubic specimens are very different from that of cylindrical ones. However, the mechanical background of these findings is unclear. As an extension of the previous laboratory study, this study performs numerical SHPB tests of cubic and cylindrical concrete specimens subjected to uniaxial impact load with the validated numerical model. The stress states of cubic specimens in relation to its failure mode under different strain rates is analyzed and compared with cylindrical specimens. The detailed analyses of the numerical simulation results show that the lateral inertial confinement of the cylindrical specimen is higher than that of the cubic specimen under the same strain rates. For cubic specimen, the corners are more severely damaged because of the lower lateral confinement and the occurrence of the tensile radial stress which is not observed in cylindrical specimens. These results explain why the dynamic material strengths obtained from the two types of specimens are different and are strain rate dependent. Based on the simulation results, an empirical formula of conversion factor as a function of strain rate is proposed, which supplements the traditional conversion factor for quasi-static material strength. It can be used for transforming the dynamic compressive strength from cylinders to cubes obtained from impact tests at different strain rates.

Frequency-related viscoelastic properties in high translucent CAD-CAM resin-based composites

ObjectiveThe study aims to quantify the viscoelastic properties of representative dental CAD/CAM resin-based composites (RBC) and to determine the effects of loading frequencies on the viscoelastic material response in comparison to clinically established CAD/CAM glass ceramics. MethodsEight RBCs, one leucite-reinforced, and one lithium disilicate glass-ceramics were selected. The quasi-static (indentation hardness HIT, indentation modulus, EIT) and viscoelastic (storage modulus E′, loss modulus E″, loss factor tan δ) material behavior was monitored by a depth-sensing indentation test equipped with a DMA module. A low-magnitude oscillating force was therefore superimposed onto a quasi-static force (Fmax = 1000 mN) at 20 different frequencies in the range 1–50 Hz. One and multiple-way analysis of variance (ANOVA), the Tukey honestly significant difference (HSD) post-hoc tests (α = 0.05), and a Pearson correlation analysis were used for data analysis. ResultsThe quasi-static parameters increased with the crystalline phase in glass ceramics and with the amount of inorganic filler in RBCs. The tan δ, which is related to the damping capacity of a material, increased with the increasing amount of glass phase in glass ceramics or with the amount of organic phase in RBCs. A pronounced influence of the frequency on the measured parameters and their patterns of variation was observed. HIT was up to ten time higher in glass ceramics compared to RBCs and highest at the lowest frequency (1 Hz). Parameters EIT and E′ differ less and were lowest at the lowest frequency. E″ distinguished three different patterns of variation with frequency. The tan δ decreased rapidly with frequency in glass ceramics, while the decrease in RBCs was gradually. Frequency influenced stronger tan δ (p < 0.001, ηP2 = 0.85), followed by E′ (p < 0.001, ηP2 = 0.773), EIT (p < 0.001, ηP2 = 0.772), and E″ (p < 0.001, ηP2 = 0.714), and less HIT (p < 0.001, ηP2 = 0.384). ConclusionsAll materials sowed viscoelastic behavior related to their microstructure and the internal friction created by grain or interphase boundary relaxation. RBCs have better damping capabilities over a wider frequency range. The deviations from the ideal elasticity were significantly lower in the glass ceramics than in the RBCs.

Modeling of crack propagation with the quasi-static material point method

Based on the theory of multiple displacement fields, the quasi-static MPM has been extended to simulate crack behavior in this paper. Compared with the existing crack simulation methods, this new method not only avoids the meshing difficulties and complex shape functions but also supports the modeling of crack growth in an arbitrary direction. The key fracture parameters, stress intensity factors, are calculated by the interaction integral method and proved accurate through the example of a cracked plate under uniaxial tension. The crack propagation is predicted with the maximum circumferential stress criterion and applied in the simulation of a compact tension test of clay. Based on this study, the proposed method is suggested as an effective scheme for modeling soil crack behaviors that are not limited to small deformation.