Degradation Of Elastic Modulus Research Articles

Effect of Elastic Module Degradation Measurement in Different Sizes of the Nonlinear Isotropic–Kinematic Yield Surface on Springback Prediction

Commercial finite element software that uses default hardening model simulation is not able to predict the final shape of sheet metal that changes its dimensions after removing the punch due to residual stress (strain recovery or springback). We aimed to develop a constitutive hardening model to more accurately simulate this final shape. The strain recovery or balancing of residual stress can be determined using the isotropic hardening of the original elastic modulus and the hardening combined with varying degrees of elastic modulus degradation and the size of the yield surfaces. The Chord model was modified with one-yield surfaces. The model was combined with nonlinear isotropic–kinematic hardening models and implemented in Abaqus user-defined material subroutine for constitutive model (UMAT). The Numisheet 2011 benchmark for springback prediction for DP780 high-strength steel sheet was selected to verify the new model, the Chord model, the Quasi Plastic-Elastic (QPE) model, and the default hardening model using Abaqus software. The simulation of U-draw bending from the Numisheet 2011 benchmark was useful for comparing the proposed model with experimental measurements. The results from the simulation of the model showed that the new model more accurately predicts springback than the other models.

Determining the coefficients of a homogeneous anisotropic hardening model for ultrathin steel sheets

In the present work, the constitutive description of a 0.1-mm-thick ferritic stainless steel sheet was optimized for application to springback simulations after bending. Springback simulations require Bauschinger effects to be characterized carefully, which is a challenging task with an ultrathin sheet. The coefficients of the homogeneous anisotropic hardening (HAH) distortional plasticity model were calibrated with Zang's novel approach based on three-point bending conducted on pre-strained sheets (Zang et al., 2014). The Hockett–Sherby isotropic hardening law and the Yld2000-2d non-quadratic yield function were considered in this work to complete the HAH approach. Moreover, the degradation of elastic modulus was also accounted for in the finite-element simulations. The coefficients of the HAH model were calibrated using an inverse method by minimizing the difference between experimental and predicted specimen profiles after three-point bending and springback of pre-strained sheets. To validate the coefficients determined with this three-point bending test, U-draw bending tests were conducted and finite-element simulations were carried out. The springback predictions were found to agree well with the experimental results for all three pre-strains investigated, namely, 0% (as-received material) and 7.5% and 12.5% pre-strained ferritic stainless steel sheets.

Evaluation and Modelling of the Reconstituted Clays Considering Pre-peak Stiffness Degradation

In this study, two clay samples, Kathmandu clay and Marine clay, were reconstituted with ordinary portland cement to study the stiffness degradation behaviour of cement mixed clay. Samples were prepared using 5%, 10% and 15% of cement to the mass of dry soil while other parameters were kept constant. The study reveals that cementation changes the strength and stiffness of the soils. The shear strength parameters of soil increase with the increase in cement content. Similarly, the initial stiffness of the clay increases with increase in cement content. Degradation of the stiffness during shearing is studied and simple equations for elastic modulus and modulus degradation of the cemented soils are proposed. Based on these relations, new stiffness degradation model is established and the predictability of the model is compared with the existing model. The comparison revealed that the prediction of the model is more accurate in determining the compression behaviour than the existing model for stiff clay.

Effect of Fibers on High-Temperature Mechanical Behavior and Microstructure of Reactive Powder Concrete.

This study was aimed to investigate the effect of steel, polypropylene (PP), and hybrid (steel + PP) fibers on high-temperature mechanical properties of reactive powder concrete (RPC). The mechanical properties considered are cubic compressive strength, axial or prismatic compressive strength, split-tensile strength, flexural strength, elastic modulus, peak strain, and stress-strain behavior. The strength recession due to high temperature was investigated at micro level by scanning electron microscope, energy dispersive X-ray spectroscopy, X-ray diffraction, mercury intrusion porosity, thermogravimetric, and differential scanning calorimetry analyses. The high-temperature tests were carried out at target temperatures of 120, 300, 500, 700, and 900 °C. The hot-state compressive strength of RPC started to decrease at 120 °C; however, a partial recovery at 300 °C and a gradual decrease above 300 °C were observed. The degradation of split-tensile strength, flexural strength, and elastic modulus were gradual with increasing temperature despite the effect of different fibers. Whereas, the peak strain was gradually increasing up to 700 °C. However, after 700 °C, it remained unchanged. Steel fiber reinforced RPC (SRPC) and hybrid fiber reinforced RPC (HRPC) showed a ductile behavior. PP fiber reinforced RPC (PRPC) showed a quite brittle behavior up to 300 °C; however, further heating made the microstructure porous and it became ductile too. Overall the performance of SRPC and HRPC were superior to PRPC because of higher modulus of elasticity, higher strength, and better fire resistance of steel fibers. Fiber reinforced RPC was found to have better fire resistance than traditional types of concrete based on comparative studies with the provisions of design codes and earlier research. The constitutive equations developed can be utilized in computer programs for structural design of RPC structures exposed to fire.

Effect of constitutive model on springback prediction of MP980 and AA6022-T4

Springback simulation of stamped sheet metal components using finite element method depends on the accuracy of appropriate material models and consideration of appropriate experimental strategies. In this work, tension-compression tests with different strategies, e.g. tension-compression, compression-tension up to various strain levels and multicycle compression-tension tests were conducted to determine parameters of the Yoshida-Uemori (Y-U) nonlinear dynamic hardening model using optimization analysis software LS-OPT. Finite element simulations with LS-DYNA were performed to predict springback behavior of both the advanced high strength steel MP980 (a 980 MPa grade multiphase steel) and aluminum alloy 6022-T4, which was then compared to measurements of stamped U-channel specimens. Results suggest that although the various tension-compression testing strategies can significantly affect the determined values of Yoshida-Uemori model parameters, springback prediction accuracy with this model does not depend on the associated variation of model parameters, at least for the two-dimensional sidewall curl of a U-channel shape. For materials (e.g. MP980) exhibiting a clear Bauschinger effect but insignificant texture anisotropy, the selection of suitable yield criteria (e.g. Hill48), the consideration of elastic modulus degradation combined with the Y-U model can obviously increase the accuracy of springback prediction. In contrast, materials (e.g. AA6022-T4) that exhibit little Bauschinger effect but have significant texture anisotropy, the use of a yield criterion that accounts for anisotropy (e.g. YLD2000-2D) is more important for improving the accuracy of springback prediction.

Two-dimensional Modelling of Thermal Responses of GFRP Profiles Exposed to ISO-834 Fire

In the past three decades, one-dimensional (1-D) thermal model was usually used to estimate the thermal responses of glass fiber-reinforced polymer (GFRP) materials and structures. However, the temperature gradient and mechanical degradation of whole cross sections cannot be accurately evaluated. To address this issue, a two-dimensional (2-D) thermo-mechanical model was developed predict the thermal and mechanical responses of rectangular GFRP tubes subjected to one-side ISO-834 fire exposure in this paper. The 2-D governing heat transfer equations with thermal boundary conditions, discretized by alternating direction implicit (ADI) method, were solved by Gauss-Seidel iterative approach. Then the temperature-dependent mechanical responses were obtained by considering the elastic modulus degradation from glass transition and decomposition of resin. The temperatures of available experimental results can be reasonably predicted. This model can also be extended to simulate the thermo-mechanical responses of beams and columns subjected to multi-side fire loading, which may occur in real fire scenarios.

Evolution and characterization of cyclic thermal shock-induced thermomechanical damage in oxide/oxide ceramics matrix composites

Thermal shock is a typical loading case for high temperature components in turbines. The ceramic matrix composites become attractive for their high temperature behavior. However, their low heat conductivity makes thermal shock damage a typical damage mechanism for the turbine application. In the present paper, microstructural evolutions of the oxide/oxide ceramic matrix composite under thermal shock are studied experimentally. The mechanical behavior is related to the thermal shock temperature and cycles. The thermomechanical damage is characterized by degradation of the macroscopic elastic modulus. A thermal shock damage model is introduced based on the continuum damage mechanics principle, which can describe monotonic as well as cyclic thermal shock damage processes.

A mechanical degradation model for bidirectional natural fiber reinforced composites under hydrothermal ageing and applying in buckling and vibration analysis

Abstract Natural fiber reinforced composites may have a great potential applications in the automotive and aerospace industries. Hydrothermal ageing in natural fiber reinforced composites leads to significantly degradation of their mechanical properties. This paper proposes a theoretical model for predicting the mechanical responses of bidirectional natural fiber reinforced composites under hydrothermal loading. Nine elastic coefficients of orthotropic composites after hydrothermal reaction and moisture absorption are obtained. Based on the present model, closed-form solutions for buckling load and frequency of a simply supported composite plate are derived. It is found that the elastic module and buckling load decrease monotonously with time, and approaches to a certain value with time. However, the frequency decreases with time firstly, and then increases with time, finally approaches to a certain value with time. In addition, the degradation of elastic modulus, buckling load and frequency for the composites with high fiber content are larger than those with low fiber content. This research may be helpful for designing natural fiber reinforced composites for applications in humid environments.

Degradation of the elastic modulus of cement-based grouting material with early ages after fire

This paper presents a comprehensive experimental investigation on the degradation of the elastic modulus of cement-based grouting materials with different early curing ages after exposed to high temperature. The research focused on the influences of different temperatures, curing ages, water mixing ratio and cooling methods on the residual elastic modulus of the material. Test results indicate that the residual elastic modulus of cement-based grouting material reduces significantly after heating. The degradation of the residual elastic modulus of the material increases with increasing water mixing ratio. However, the influence of water mixing ratio is not very significant. The research indicates that the models proposed in Eurocode 2, the Chinese code and ACI-216 for normal concrete are not suitable to predict the degradation of the residual elastic modulus of cement-based grouting materials exposed to fire.

Kinematic hardening performance of 5052 aluminium alloy subjected to cyclic compression-tension

In order to study the kinematic hardening performance of 5052 aluminium alloy, experiments of cyclic compression-tension were conducted in this work. The kinematic hardening performance including the Bauschinger effect, transient hardening and permanent softening shown by the forward-reverse stress-strain curves was discussed. The famous Yoshida-Uemori hardening model was adopted to characterize the kinematic hardening behaviour of AA5052. The parameters in Yoshida-Uemori hardening model were identified with an inverse method composed by experiments, finite element simulation and optimization. Experiments of cyclic loading-unloading uniaxial tension were also performed to identify the degradation of the elastic modulus of AA5052 with the plastic strain. U-bending springback simulation using the Yoshida-Uemori hardening model was conducted. The results showed that the investigated AA5052 has strong Bauschinger effect, transient hardening and permanent softening. The percentage of elastic modulus degradation could reach 16.7% at 8.8% plastic strain. The Yoshida-Uemori hardening model can capture the kinematic hardening behaviour of AA5052 very well.

Evaluation of Gas Migration and Rock Damage Characteristics for Underground Nuclear Waste Storage Based on a Coupled Model

In the deep geological repository of nuclear waste, the corrosion of waste generates gas, which increases the storage pressure, changes the properties of the rock strata, and affects the stability of nuclear waste repository. Therefore, it is of great importance to understand the gas migration in the engineering barrier and the potential impact on its integrity for the safety assessment of nuclear waste repository. A hydro-mechanical-damage model for analyzing gas migration in sedimentary rocks is established in this paper. On the basis of which, a set of coupled formulas for the coupling of gas migration in rock mass is established. The model considers the characteristics of gas migration in sedimentary rock, especially the microcracks caused by the degradation of elastic modulus and damage, and the coupling between the rock deformation and failure of fractures. The numerical simulation of gas injection test is beneficial to understand the mechanism of gas migration process in sedimentary rock.

Strain-Softening Model for Marble Considering the Degradation of Elastic Modulus

Rocks encountered in deep underground engineering, such as coal mining and tunnel excavating applications, are usually in states of failure. It is of great engineering significance to study the post-peak strength behavior of rock. A strain-softening model that considers the degradation of elastic modulus was suggested in this article. The strain-softening characteristics and degradation law of the elastic modulus for marble were first obtained based on triaxial cyclic loading tests. A strain-softening model was then suggested by considering the degradation of the elastic modulus. Finally, the suggested model was embedded in the finite difference software (FLAC), and the conventional triaxial compression tests for marble were simulated. The results showed that the stress–strain curves simulated using the suggested model were in agreement with the contour curves of cyclic loading. The results may serve as a reference for the strain-softening characteristics of the Jinping marble studied in this paper.

Use of nanoindentation phase characterization and homogenization to estimate the elastic modulus of heterogeneously decalcified cement pastes

Nanoindentation phase characterization is used with a homogenization method to estimate the macroscopic response of heterogeneous, multiphase materials with large chemically-induced gradients from their measured micromechanical properties. The method was applied to predict the macroscopic response of a non-uniformly degraded cement paste from leaching-induced decalcification by ammonium nitrate under 3-dimensional exposure conditions. Coupled nanoindentation with scanning electron microscopy and energy dispersive x-ray spectroscopy constitutive phase elemental analysis was used to link the mechanical response at each nanoindentation location to chemical composition and relate the mechanical phases identified statistically by Gaussian deconvolution to the chemical phases present in the microstructure. The nanoindentation phase characterization-based micro-macroscale upscaling method provided quantitative characterization of the relationship between microstructure evolution and mechanical properties as a function of chemical changes. The calculated homogenized elastic moduli of the reference and decalcified cement pastes ranged from 24.2–31.2 GPa and 9.2–11.7 GPa, respectively, and were of similar magnitude to the dynamic elastic moduli measured experimentally (31.1 ± 0.9 GPa and 13.7 ± 1.7 GPa, respectively). Furthermore, the degradation of the cement paste macroscale elastic modulus was controlled by the decalcification of the calcium-silicate-hydrate phases and the mechanical properties of the most prominent zone of the material.

Dependence of plastic strain and microstructure on elastic modulus reduction in advanced high-strength steels

Increase in the use of the advanced high-strength steels (AHSS) is an interesting alternative to automotive industry to reduce vehicle weight and fuel consumption. However, it has been limited due to challenges in formability, tool life, and springback. The springback is pointed in the literature as one of the challenges that involves the mass production of structural components and the aspects that shows influence are still not fully understood. There is still a gap in the literature to analyze the elastic modulus variation during unloading (also called chord modulus). Therefore, this study experimentally examines the variation of elastic modulus in conjunction with plastic strain and initial microstructure of various automotive steels. For all AHSS, it was found that the elastic modulus decreases during loading and unloading with respect to plastic strain. It was observed that the microstructure of AHSS greatly affects the reduction in elastic modulus upon deformation. It was also found that the degradation of elastic modulus also affected by the anisotropy of the material.

Unified constitutive model with consideration for effects of porosity and its application to polyurethane foam

Abstract Polyurethane foam (PUF) is a popular insulation material and has crucial mechanical characteristics under compression in the principal loading direction, including nonlinear behavior dependent on strain rate and temperature, degradation of elastic modulus, and decrease of void fraction. Additionally, its insulation performance relies on the blowing agents in voids. These material characteristics enable the evaluation of the structural integrity and performance of PUF insulation systems, if the prediction of these characteristics and the relationship between change in void fraction and insulation performance are possible. In this paper, a unified constitutive model was proposed for this purpose. This model was verified with corresponding experimental results, and the validation showed that the material characteristics can be depicted successfully. Moreover, for the sake of applicability, the model was used in the evaluation of the insulation system in an LNG Carrier.

Effects of squeeze-off on mechanical properties of polyethylene pipes

Squeeze-off is a common practice in industry to shut off or reduce gas flow in polyethylene (PE) pipe. In this study, influence of squeeze-off on degradation of mechanical properties for PE pipe was examined. Three squeezing speeds of 0.01, 1 and 50 mm/min were used to cover the possible squeeze-off scenarios that may be encountered during the pipe repair or maintenance. Results show that squeeze-off of PE pipe causes significant degradation in elastic modulus and yield strength, with the maximum reduction of 82% for elastic modulus and 27% for yield strength. Furthermore, contradictory to the common belief that slower is better, reducing the squeezing speed was found to have no effect on the extent of property degradation. In view of those findings, a study was conducted using mechanical testing and finite element (FE) simulation to elucidate the damage evolution in PE pipe in different loading modes (including tension and compression) and with different loading history (in terms of maximum pre-strain level and loading speed). Results show that both tensile and compressive loading modes can cause severe degradation in elastic modulus and yield strength. The results also show that under a single loading mode, the extent of damage at a given pre-strain level is indeed a function of loading rate. However, in a pipe which has been squeezed to subject the pipe wall to a combined tensile and compressive stresses, degradation of the “apparent” elastic modulus and yield strength, defined as their equivalent values for a given wall thickness, becomes insensitive to the loading rate.

A rate-independent continuum model for bone tissue with interaction of compressive and tensile micro-damage

Low bone strength is a major risk factor for osteoporotic fractures and is only partially determined by clinical densitometry. Accumulated micro-damage induces residual strains, degrades elastic modulus and reduces bone strength independently of bone mineral density. Histologically, overloading of bone in compression and tension leads to distinct crack size, distribution and orientation which interact during combined loading scenarios. Statistics of rheological models can describe this process and reproduce experimental stress-strain curves with an unprecedented realism, but are computationally expensive and therefore difficult to generalize to 3D. Accordingly, the aim of this work is to formulate a continuum damage model that describes the key features of bone micro-damage, namely the accumulation of residual strains, the degradation of elastic modulus and the reduction of strength in compression, tension and especially in their sequential application. The promising qualitative agreement of the model with the experiments will motivate a generalization to 3D and allow the biomechanical investigation of bones and bone-implant systems subjected to cyclic overloading in tension and/or compression.

Mechanical properties of cerium oxide-modified vulcanised natural rubber at elevated temperature

ABSTRACTCerium oxide (CeO2) was used as the reinforcement filler to improve the mechanical properties of rubbers. Rubber components are often used at high temperature, so the mechanical properties of CeO2-modified vulcanised natural rubbers (NR/CeO2) were investigated at elevated temperatures. The tensile properties, stress relaxation and creep recovery response were studied from 30°C to 150°C. NR/CeO2 demonstrated higher crosslink density and elastic modulus. The degradation of elastic modulus could be alleviated in the NR/CeO2 at elevated temperatures. Moreover, a remarkable enhancement in stress relaxation resistance and creep resistance was achieved in the NR/CeO2 at elevated temperatures. The improved stress relaxation resistance and creep resistance were attributed to the enhanced interaction and bonding force of rubber chains caused by CeO2 filler. CeO2 was an effective reinforcement filler to improve the mechanical properties of NR at elevated temperatures.

Damage Assessment Using Information Entropy of Individual Acoustic Emission Waveforms during Cyclic Fatigue Loading

Information entropy measured from acoustic emission (AE) waveforms is shown to be an indicator of fatigue damage in a high-strength aluminum alloy. Three methods of measuring the AE information entropy, regarded as a direct measure of microstructural disorder, are proposed and compared with traditional damage-related AE features. Several tension–tension fatigue experiments were performed with dogbone samples of aluminum 7075-T6, a commonly used material in aerospace structures. Unlike previous studies in which fatigue damage is measured based on visible crack growth, this work investigated fatigue damage both prior to and after crack initiation through the use of instantaneous elastic modulus degradation. Results show that one of the three entropy measurement methods appears to better assess the damage than the traditional AE features, whereas the other two entropies have unique trends that can differentiate between small and large cracks.

Understanding indentation-induced elastic modulus degradation of ductile metallic materials

Noticeable degradation of the measured elastic moduli of ductile metals has been found in meso-/macro- indentation tests. Although this phenomenon has been exploited to estimate the fracture properties of ductile metallic materials, the mechanism of the indentation-induced damage is rarely studied. Finite element simulations show that the finite stiffness of an indentation system can cause a false degradation of the effective indentation modulus. However, the decay pattern is different from that due to the indentation damage. Through theoretical analysis and experimental measurements, it is shown that the elasticity degradation can be mainly attributed to the anisotropic damage caused by the shear deformation in the indentation test.