Nonlinear Stress-strain Curves Research Articles

Strain Rate Dependence and Short-Term Relaxation Behavior of a Thermoset Polymer at Elevated Temperature: Experiment and Modeling

The inelastic deformation behavior of polymerization of monomeric reactants-15 (PMR-15) neat resin, a high-temperature thermoset polymer, was investigated at 288°C. The experimental program was designed to explore the influence of strain rate changes in the 10−6–10−3 s−1 range on tensile loading, unloading, and strain recovery behavior, as well as on the relaxation response of the material. The material exhibits positive, nonlinear strain rate sensitivity in monotonic loading. Nonlinear, “curved” stress-strain behavior during unloading is observed at all strain rates. The strain recovery at zero stress is profoundly affected by prior strain rate. The prior strain rate is also found to have a strong influence on relaxation behavior. The rest stresses measured at the termination of relaxation tests form the relaxation boundary, which resembles a nonlinear stress-strain curve. The results suggest that the inelastic behavior of the PMR-15 solid polymer at 288°C can be represented using a unified constitutive model with an overstress dependence of the inelastic rate of deformation. The experimental data are modeled with the viscoplasticity theory based on overstress. A systematic procedure for determining model parameters is presented and the model is employed to predict the response of the material under various test histories.

Fatigue life simulation of multi-axial CFRP laminates considering material non-linearity

The objective of an on-going DFG research project is to investigate the effect of non-linear stress–strain curves (e.g. τ 12– γ 12) on the fatigue life simulation of carbon fiber reinforced polymer (CFRP) laminates under variable amplitude cyclic loading. Based on the critical element concept of Reifsnider and Stinchcomb appropriate models including a secant modulus iteration for the non-linear stress analysis, the evaluation of inter-fiber fracture effects applying a fracture plane criterion, and appropriate continuum mechanics based stiffness degradation algorithms to treat both inter-fiber cracking and ply delamination were implemented into an existing fatigue life prediction software. Using this software the fatigue life of a quasi-isotropic vinylester/urethane/carbon fiber composite laminate subjected to miniTWIST variable amplitude loading was analyzed and compared to experimental data.

Micromechanics-Based Predictions on the Overall Stress-Strain Relations of Cement-Matrix Composites

A micromechanics-based model is proposed to determine the nonlinear stress-strain relations of cement-matrix composites at different concentrations of inclusions (aggregates). We first conducted some experiments to uncover the stress-strain behavior of the cement paste with a water-to-cement ratio of 0.45, and those of the mortar with the same cement paste but at three different volume concentrations of aggregates. The behavior of the cement paste is then simulated by Burgers’ rheological model. In the development of the composite model, we extend the linear elastic response to the nonlinear one through the replacement of elastic moduli by the corresponding secant moduli. The nonlinear stress-strain curves of the cement-matrix composite are then determined from those of the cement paste and inclusions. It is shown that the predicted stress-strain curves of the mortar are in close agreement with the experimental curves up to an aggregate volume fraction of 49% or 60 wt % .

Stress block parameters for concrete flexural members reinforced with superelastic shape memory alloys

The unique properties of superelastic shape memory alloys (SMAs) have motivated researchers to explore their use as reinforcing bars. The capacity of a steel reinforced concrete (RC) section is calculated by assuming a maximum concrete strain ec-max and utilizing stress block parameters, α1 and β1, to simplify the non-linear stress–strain curve of concrete. Recommended values for ec-max, α1, and β1 are given in different design standards. However, these values are expected to be different for SMA RC sections. In this paper, the suitability of using sectional analysis to evaluate the monotonic moment–curvature relationship for SMA RC sections is investigated. A parametric study is then conducted to identify the characteristics of this relationship for steel and SMA RC sections. Specific mechanical properties are assumed for both steel and SMA. Results were used to evaluate ec-max, α1, and β1 values given in the Canadian standards and to propose equations to estimate their recommended values for steel and SMA RC sections.

비선형 유한요소해석을 이용한 웨더스트립의 특성예측

TPE is used as alternative for rubber, the best example is the weather strip for automobile. The nonlinear material properties of weather strip were important to predict the behaviors of weather strip. Uniaxial tension and equi-biaxial tension tests were performed to achieve the nonlinear material constant and stress-strain curves. The nonlinear material constant of weather strip is evaluated by using the nonlinear finite element analysis. In this paper, the prediction for weather strip is analyzed by using commercial finite element program, ANSYS. The nonlinear finite element analysis of weather strip is executed to predict the behavior of weather strip for automobile.

The rate (time)-dependent mechanical behavior of the PMR-15 thermoset polymer at elevated temperature

The inelastic deformation behavior of PMR-15 neat resin, a high-temperature thermoset polymer, was investigated at 288 °C. The experimental program was designed to explore the influence of strain rate on tensile loading, unloading, and strain recovery behavior. In addition, the effect of the prior strain rate on the relaxation response of the material, as well as on the creep behavior following strain-controlled loading were examined. The material exhibits positive, nonlinear strain rate sensitivity in monotonic loading. Nonlinear, “curved” stress–strain behavior during unloading is observed at all strain rates. The recovery of strain at zero stress is strongly affected by prior strain rate. The prior strain rate also has a profound influence on relaxation behavior. The rest stresses measured at the termination of relaxation tests form the relaxation boundary which resembles a nonlinear stress–strain curve. Likewise, creep response is significantly influenced by prior strain rate.

Nonlinearity, hysteresis, end-point memory, and congruence in sandstones

Very low frequency stress-strain measurements on many rocks show definite and repeatable hysteresis loops. Much of the modeling of this behavior uses Preisach or Ising-like models adapted from models developed for magnetic systems which exhibit hysteresis. To date, the experimental data on many rocks showing end-point memory are noisy and only qualitative. The congruence property, in fact, has never been examined for rocks. Just how well does the behavior of a sandstone fit a Preisach model? To find the answer to this question, we performed a new set of careful stress-strain experiments on several sandstones to examine end-point memory (in detail) and also to see if the congruence property does indeed hold for these rocks. In addition we explored the dependence of measurement rate on the relaxation time of these rocks (the analog to magnetic aftereffect). For very slow measurement rates (low frequencies), hysteresis disappears, leaving only a simple nonlinear stress-strain curve.

Forming simulation of a thermoplastic commingled woven textile on a double dome

This paper presents thermoforming experiments and FE simulations of a commingled glass-PP woven composite on a double dome geometry, with the aim of assessing the correspondence of predicted and experimental shear angles. Large local deformations - especially in-plane shear, i.e. relative rotation between the two yarn families – occur when draping a textile on a three dimensional part and eventually unwanted phenomena like wrinkling or tearing may occur. The macroscopic drape behaviour of a weave is generally subdivided into: 1) The high tensile resistance along the yarn directions, expressed as non-linear stress-strain curves, and 2) The shear resistance, expressed as non-linear shear force versus shear angle curves. The constitutive model is constituted of a dedicated non-orthogonal hypo-elastic shear resistance model, previously described in [1, 2], combined with truss elements that represent the high tensile resistance along the yarn directions. This model is implemented in a user subroutine of the ABAQUS explicit FE solver. The material parameters have been identified via textile biaxial tensile tests at room temperature and bias extension tests at 200°. Thermoforming experiments are performed on a rectangular blank with the warp direction along the second symmetry plane of the tool, with a preheating temperature of 200°C, a constant mold temperature of about 70°C, and a blankholder ring. It was concluded that the shear angles were fairly well predicted for this particular case study, which could be expected in view of the fact that no wrinkles had formed during the thermoforming experiment.

Patents on Superelastic Shape Memory Alloy

Innovative investigations, discoveries and recent patents regarding superelastic shape memory alloy (SMA), a novel material, are briefly discussed in this review paper. Known as a functional material, SMA can recover large strains in two ways: shape memory effect (SME) and pseudoelasticity. SME is by virtue of temperature induced martensitic transformation while pseudoelasticity (also called superelasticity) happens because of stress induced martensitic transformation (SIMT). SMA is one of the most widely used functional materials in many adaptive structures, as well as in medical and biomedical applications. Because of SME, SMA can be mainly used for active control of adaptive structures. On the other hand, having pseudoelasticity SMA can be used for passive damping of a vibrating structure. Superelastic SMA is also widely used for applications like: antenna of portable phones, headband of headphones, in the ballpoint pens and eyeglass frames etc. This study will focus mainly on pseudoelasticity of SMA and its potential characteristics. Keywords: Shape memory alloy, stress induced martensitic transformation, pseudoelasticity (superelasticity), nonlinear stress-strain curves, tension-compression asymmetry

Processing, damage tolerance and crack healing in the silicon carbide fabric-covered silicon carbide composite

SiC fabric with or without alumina powder was joined to the surfaces of SiC compact under the applied pressures of 5-39 MPa. The stress-strain curve, strength, damage tolerance using Vickers indentor and crack healing effect were investigated for both the SiC with and without SiC fabric layers. The strength of monolithic SiC was greatly decreased by the surface damage but easily recovered to the original strength by the healing at a relatively low temperature of 1100°C in air. When a simultaneous processing using an SiC compact covered with SiC fabric was applied, which promoted the densification of inside SiC compact, the surface SiC fabric dissolved in the liquid of sintering additives included in the SiC compact during the hot-pressing at 1950°C. The mechanical properties of this type composite were similar to those of monolithic SiC compact. The SiC fabric joined to dense SiC compact under a low applied pressure at 1300-1600°C prevented the propagation of the cracks formed by Vickers indentor and showed a significant nonlinear stress-strain curve. As a result, no change in the strength was measured before and after the introduction of cracks. However, increased joining pressure resulted in the creep rupture of dense inside SiC compact. Decrease of the joining temperature and decrease of the joining pressure were effective to increase the flexural strength.

A molecular mechanics approach for analyzing tensile nonlinear deformation behavior of single-walled carbon nanotubes

In this paper, by capturing the atomic informa- tion and reflecting the behaviour governed by the nonlin- ear potential function, an analytical molecular mechanics approach is proposed. A constitutive relation for single- walled carbon nanotubes (SWCNT's) is established to describe the nonlinear stress-strain curve of SWCNT's and to predict both the elastic properties and breaking strain of SWCNT's during tensile deformation. An analysis based on the virtual internal bond (VIB) model proposed by P. Zhang et al. is also presented for comparison. The results indicate that the proposed molecular mechanics approach is indeed an acceptable analytical method for analyzing the mechanical behavior of SWCNT's. of CNT's. The Young's modulus of CNT's was found to be about 1 TPa (2-5). Many theories of mechanics have also been proposed to study the mechanical properties of CNT's. Zhang et al. (6) developed a continuum mechanics approach to model elastic properties of single-walled carbon nanotubes (SWCNT's), and the Young's modulus of SWCNT's was pre- dicted to be 0.705 TPa. Li and Chou (7) presented a structural mechanics approach to model the deformation of CNT's, and calculated the Young's moduli for CNT's with different radii. A similar approach was presented by Chang and Gao (8), and the chirality- and size-dependent elastic properties such as Young's modulus, Poisson's ratio and shear modulus were predicted (9,10). Moreover, the nonlinear effect of SWCNT's was taken into account (11) recently. In view of the unrealistic demand of computational power to study materials of practical size, atomistic simulations are deemed unsuitable for the study of large scaled nanometer materials in large time spans. Therefore, various attempts have been made by researchers to introduce atomic character- istics into the mechanical theory. For example, the molecular mechanics originally developed by chemical scientists (12) can be considered one of the successful attempts. According to the definition of Burkert and Allinger (12), the total potential energy, U , is constitutive of several individual energy terms corresponding to bond stretching, angle bend- ing, torsion, and van der Waals interactions, respectively: U = � Ustretch + � Ubend

Improvement of Strength, Weibull Modulus and Damage Tolerance of SiC

This paper reports the significant effects of addition of 30 nm SiC, polytitanocarbosilane and SiC fabric to enhance the mechanical reliability of SiC. The flexural strengths of dense SiC hot-pressed with 800 nm particles (average strength 565 MPa for Y2O3-Al2O3 additives and 640 MPa for Yb2O3-Al2O3 additives) were enhanced to average strength 735-820 MPa by the addition of 30 nm SiC particles (25 vol%). Addition of polytitanocarbosilane (3 vol%, precursor of SiC fiber) to the bimodal SiC powder compact with Y2O3-Al2O3 additives provided more excellent mechanical properties of average strength 910 MPa, fracture toughness 5.2 MPa·m1/2 and Weibull modulus 11.3. SiC fabric and SiC (60 vol%) - Al2O3 (40 vol%) sheet of 60 micrometer thick were alternatively laminated and bonded to the surfaces of dense SiC under the pressure of 5 MPa. The SiC fabric prevented the propagation of the cracks formed by Vickers indentor and showed a significant nonlinear stress-strain curve. As a result, no change in the strength was measured before and after the introduction of cracks.

Stress-Strain Characteristics of Clay Brick Masonry under Uniaxial Compression

The uniaxial monotonic compressive stress-strain behavior and other characteristics of unreinforced masonry and its constituents, i.e., solid clay bricks and mortar, have been studied by several laboratory tests. Based on the results and observations of the comprehensive experimental study, nonlinear stress-strain curves have been obtained for bricks, mortar, and masonry and six “control points” have been identified on the stress-strain curves of masonry, which can also be used to define the performance limit states of the masonry material or member. Using linear regression analysis, a simple analytical model has been proposed for obtaining the stress-strain curves for masonry that can be used in the analysis and design procedures. The model requires only the compressive strengths of bricks and mortar as input data, which can be easily obtained experimentally and also are generally available in codes. Simple relationships have been identified for obtaining the modulus of elasticity of bricks, mortar, and ...

Development and validation of numerical model of steel fiber reinforced concrete for high-velocity impact

This paper employed hydrodynamic finite element code LS-DYNA to study the dynamic response of steel fiber reinforced concrete (SFRC) subject to impact loading. The elastic–plastic hydrodynamic material model was employed to model the non-linear softening behavior of SFRC by tabulated stress–strain curve. Uniaxial compression test and split test were performed to obtain the material properties and non-linear stress strain curve of SFRC. A simple way to determine the element erosion parameters is proposed in this paper. The residual velocity of projectile and the scabbing diameters on the rear surface of SFRC target predicted by proposed method show well agreement with the experimental results. The proposed methodology is useful and efficient can be further developed for designing the protection of military structures, nuclear power plants and other facilities against high-velocity projectiles.

Characterization and strength modeling of parallel-strand lumber

Abstract The current work expands on a three-dimensional, non-linear, stochastic finite-element model previously developed by the author. The model predicts a materially non-linear stress-strain curve for tension, compression and bending scenarios. It is based on the non-linear constitutive properties of the individual strands, which are characterized within the framework of orthotropic elasto-plasticity. The constitutive model employs the Tsai-Wu yield criterion and an associated flow rule. Failure is marked by an upper bound surface whereupon either perfect plasticity or an abrupt loss of strength and stiffness ensues. The finite element code has also extended the capacity to perform Monte Carlo simulations. The model was further developed to predict the mechanical behavior of parallel-strand lumber (PSL) made from Douglas fir. The physical features of PSL were measured and incorporated into the finite element model and the mechanical behavior of PSL was simulated. Statistical distributions for macroporosity and grain angle variation in PSL were created and included in the model as individual random variables in a stochastic and probabilistic manner. Constitutive curves for PSL were numerically generated under tensile, compressive and three-point bending conditions. Comparison of the computed and experimental data sets demonstrates the validity of the proposed modeling technique.

Nonlinear analysis of cantilever shape memory alloy beams of variable cross section

Cantilever beams, made of shape memory alloy (SMA), undergo much larger deflection incomparison to those made of other materials. Again, cantilever beams with reducingcross section along the span show much larger deflections compared to thoseof constant cross section beams. Analysis was conducted for such a cantileverbeam with reducing cross-sectional area made of SMA, taking into account itshighly nonlinear stress–strain curves. A computer code in C has been developedusing the Runge–Kutta technique for the purpose of simulation. For rigorousanalysis, the true stress–strain curves in tension as well as in compression have beenused for the study. Moment–curvature and reduced modulus–curvature relationsare obtained from the nonlinear stress–strain relations for different sections ofthe beam and used in the simulation. It is seen that load–deflection curves areinitially linear but nonlinear and convex upward at a high load. Furthermore,the compressive stress in the beam is significantly higher than the tensile stressbecause of asymmetry. Interestingly, for the different cases considered, it is foundthat part of the SMA beam material may remain in the parent austenite phase,mixed phase or in the stress-induced martensitic phase. Importantly, it is foundthat more material can be removed from an SMA beam of uniform strength,originally designed without considering geometric nonlinearity and the effect ofend-shortening. Comparison of the numerical results with the available theory showsvery good agreement, verifying the soundness of the entire numerical simulationscheme.

Nonlinear Behavior in Compression and Tension of Thermally Sprayed Ceramic Coatings

Mechanical properties of thermally sprayed coatings, especially of ceramics, are strongly influenced by a high density of mesoscopic defects, microcracks of dimensions between fractions of μm up to tens of μm. The anisotropic linear elastic stress–strain relations are valid only at very low deformations, e.g., |e| < 0.05%, with small values of Young’s moduli due to elastic openings and elastic partial closings of microcracks. At higher deformations, e.g., 0.05% < |e| < 0.4%, the stress–strain relations are strongly nonlinear. Under compressive stresses, elastic closing of microcracks leads to a gradual decrease of the microcrack density and to an increase of Young’s modulus in compression. Under tensile stresses, the microcracks slightly grow by inelastic processes; the microcrack density gradually increases and effective Young’s modulus in tension decreases. A two-parametric equation containing linear and quadratic terms is used to describe the nonlinear stress–strain curves of plasma-sprayed ceramic coatings. The effect of nonlinearity on the bending of beams with coatings and the nonlinear combination of external and residual stresses are discussed. The fracture of coatings at higher tensile stresses due to coalescence of the microcracks is mentioned.

OS15-3-4 Improved Rail Shear Method of ASTM D4255/D4255M for Cyclic Shear Tests of Fibrous Composites

This paper presents an improved rail shear method of ASTM D 4255/D4255M and the design procedure of new fixture for low cyclic shear loading. This fixture is designated to determine mechanical properties of in-plane shear modulus, nonlinear shear stress-strain curves, shear strength and visco-elastoplastic behaviour of fibrous composites under cyclic shear loads. A series of experiments have been carried out using the new rig to determine shear stress-strain response of unidirectional fibre reinforced laminated specimens under various cyclic loading conditions. An FE simulation has been conducted using a commercial code ABAQUS and its user subroutine UMAT to define nonlinear material behaviour as a verification of the accuracy of the new Cyclic Rail Shear Fixture (CRSF).

亀裂の緩進展による引張破壊―岩盤内の均質化亀裂進展（第４報）―

A macroscopic tension fracture of rock is analyzed as a result of the sub-critical crack growth in it, and a numerical procedure for the failure prediction is presented and discussed, basing upon the critical pressure-crack elongation curve (pc—a curve) for the pure mode I crack propagation (KII = 0, KI = KIC) in the homogenized joint model, which is accurately evaluated by means of the Stress Compensation-Displacement Discontinuity Method (SC-DDM). The crack elongation rate (da/dt) is formulated by the empirical equation of the form of da/dt ∝ KIn, where n: the sub-critical crack growth index. Computing the applied stress-crack elongation curves (p—a curves), the rate-dependent failure of rock in the tension test is concretely analyzed along with the time-dependent failure of rock in the creep test. The significant correlation between these experiments is discussed by comparing the non-linear stress-strain curves of the tension test to the non-linear time-strain curves of the creep test. It is clarified that the non-linearity is deeply associated with the sub-critical crack growth.

A biphasic viscohyperelastic fibril-reinforced model for articular cartilage: Formulation and comparison with experimental data

Experiments in articular cartilage have shown highly nonlinear stress–strain curves under finite deformations, nonlinear tension–compression response as well as intrinsic viscous effects of the proteoglycan matrix and the collagen fibers. A biphasic viscohyperelastic fibril-reinforced model is proposed here, which is able to describe the intrinsic viscoelasticity of the fibrillar and nonfibrillar components of the solid phase, the nonlinear tension-compression response and the nonlinear stress–strain curves under tension and compression. A viscohyperelastic constitutive equation was used for the matrix and the fibers encompassing, respectively, a hyperelastic function used previously for the matrix and a hyperelastic law used before to represent biological connective tissues. This model, implemented in an updated Lagrangian finite element code, displayed good ability to follow experimental stress–strain equilibrium curves under tension and compression for human humeral cartilage. In addition, curve fitting of experimental reaction force and lateral displacement unconfined compression curves showed that the inclusion of viscous effects in the matrix allows the description of experimental data with material properties for the fibers consistent with experimental tensile tests, suggesting that intrinsic viscous effects in the matrix of articular cartilage plays an important role in the mechanical response of the tissue.