Plastic deformation and damage of polyoxymethylene in the large strain range at elevated temperatures

The deformation behaviour of polyoxymethylene has been studied in plane strain compression at temperatures from 120 °C up to 165 °C and in uniaxial tension and simple shear at 160 °C for strain rates from 10⁻⁴ to 1 s⁻¹. In uniaxial tension the stress-strain behaviour was determined by a novel video-controlled testing system. The measurements showed that there was a very significant evolution of volumetric strain, indicating that damage mechanisms play a key role in the plastic deformation behaviour.All tests showed similar deformation stages with a short region of visco-elastic behaviour followed by a rounded yield point. The von Mises equivalent yield stress for these tests showed a linear relationship with logarithmic strain rate, suggestive of an Eyring type thermally activated process. After yielding, all stress-strain curves showed a long plastic deformation regime, which in shear occurred at constant stress. In plane strain compression there was also only a very small increase in stress, in contrast to uniaxial tension where very significant strain hardening was observed at high strains, which is attributed to the onset of structural changes.     

Highlighting delayed elastic processes at zero stress in a polymer glass

The present study highlights the existence of a post‐evolution of the fracture and damage in glassy polymers at zero‐stress relaxation evidencing that the dynamic is not frozen below the glass transition but that it releases at zero stress in the plastic regime from past stresses. The observation of a further evolution of the glass without applied stress (at zero stress) is unexpected and inaccessible using conventional tensile tests since they are not designed to enable a zero‐stress measurement. Non‐contact methods such as confocal microscopy and autocorrelation analysis are used to examine polymethylmethacrylate samples plastically deformed (up to 8% elongation rate) and subsequently studied in the unloaded state. The zero‐stress evolution is morphologically characterized by a nucleation of new microfractures and an evolution of the existing cracking. The analysis of the image correlation indicates that the strain field continues to evolve revealing an intermittent retraction of the displacement field at time scales up to several days. Different temperatures from ?75 °C up to ?45 °C below the glass transition have been tested and prove that the retraction process is thermally activated. The retraction process (about 1% ? 2% of the deformation rate) implies that plastic deformation does not relax completely from anterior stresses but exhibits a delayed elasticity. These properties have profound consequences impacting the future physical and mechanical properties of the material. © 2015 Society of Chemical Industry     

Dissipation and resilience of elastomeric segmented copolymers under extreme strain rates

The high strain rate behavior of elastomeric segmented copolymers has received significant attention in recent years in connection with the design of polymeric composites for a myriad of engineering and military applications. The presence of thermodynamically immiscible phases of hard and soft domains in these copolymeric materials enables multiple energy storage and dissipation pathways which offer new avenues towards highly resilient yet dissipative protective systems. In this research, the extreme strain rate behavior of an exemplar polyurea is addressed in Taylor impact tests to quantify ultrafast deformation processes at strain rates over 10⁵/s which are incurred in ballistic and blast loading events. Numerical simulations of the high rate, inhomogeneous deformation incurred during Taylor impact tests are conducted using a recently proposed large deformation constitutive model implemented within nonlinear finite element simulations. The simulations show the predictive capability of the viscoelastic–viscoplastic constitutive model under extreme strain rate events and reveal the details of the evolution of the deformation and stress waves during impact loading. Additionally, the highly dissipative yet resilient features of polyurea under inhomogeneous deformation at extreme strain rates are elucidated in terms of energy dissipation and shape recovery by taking representative sets of constitutive models for rubbery and glassy polymers and their combinations. The remarkable ability of the polyurea to dissipate energy in a manner similar to a glassy thermoplastic yet exhibits the resilience of a rubbery material is shown in both the experiments and the models. This work reveals that the model of the two-phase structures of segmented copolymers is providing both dissipation and energy storage pathways under extreme deformation.     

Thermally activated deformation under Knoop indentations in super-hard directions of high-quality synthetic type-IIa diamond crystals

The deformation resistance at room temperature against a Knoop indentation in (001)<110> (the<110> direction on the (001) plane) of high-quality synthetic type-IIa diamond is known to be extremely high. The behavior of deformation in the hard direction activated thermally by heating was investigated, using super-hard Knoop indenters prepared from high-quality diamond crystals by taking the tip orientation to (001)<110>. Indentation tests in (001)<110> with a load of 4.9 N revealed that the formation of normal Knoop impressions arises suddenly at a threshold temperature of 200–240 °C, whereas no impressions are observed up to 200 °C. The hardness values derived from the impressions in (001)<110> formed above the threshold temperatures are as low as 50–60% those in (001)<100> at the same temperatures. The anisotropy in the Knoop hardness at such high temperatures is consistent with the nature of anisotropy predicted by an effective resolved shear stress model for a {111}<110> slip deformation.     

Strain‐rate and temperature effects on the deformation of polypropylene and its simulation under monotonic compression and bending

Monotonic compressive loading and bending tests are conducted for solid polypropylene (PP) under constant or time‐varying strain‐rates and temperatures of 10, 25, 40°C. The observed compressive stress‐strain responses under constant conditions have revealed that the inelastic deformation behavior is remarkably dependent on loading rates and temperatures of normal use. The examination of such inelastic behavior has indicated that the strain‐rate effects correspond with the temperature effects based on the concept of time‐temperature equivalence. The viscoplastic constitutive theory based on overstress (VBO) has successfully reproduced the experimental responses with stress‐jumping phenomena using the equivalent time. Four‐point bending tests are performed under monotonic loading and holding for PP beams at three different temperatures. The observed deformation behavior has shown that the Bernoulli‐Euler hypothesis is valid. The VBO model and beam bending theory has generated the basic equations for PP beams, showing an analogy with the uniaxial one. In the numerical analysis, the equations are transformed into nonlinear ordinary differential equations with use of Gaussian quadrature for the spatial integrals. The comparison of numerical and experimental results has suggested some modifications for actually loaded moment taking the effect of deflection and friction into consideration. Finally, the numerical calculation has simulated the experimental time‐histories of curvatures fairly well.     

Energy storage during inelastic deformation of glassy polymers

In this paper, aspects of the microstructural state of glassy polymers that evolve during physical ageing and inelastic deformation were studied. Differential scanning calorimetric (d.s.c.) measurements were performed on specimens of three glassy polymers: polystyrene (PS), polycarbonate (PC) and poly(methyl methacrylate) (PMMA). Materials were subjected to both a quenched and a well annealed heat treatment and subsequently deformed in compression to various levels of strain. Stress-strain curves and companion d.s.c. scans were compared.

The well known enthalpy overshoot at T_g was observed for the annealed samples, showing that ageing is accompanied by enthalpy relaxation. The annealed material was also found to require a higher stress to yield, and the additional work required to strain-soften the annealed polymer to the flow stress level of its quenched companion was found to correlate well with the area of the enthalpy overshoot of the annealed specimen.

Inelastic deformation was found to increase the specific enthalpy of both annealed and quenched specimens. In the annealed material, the enthalpy overshoot at T_g was found to decrease with inelastic strain and was completely erased by about −20% strain. Simultaneously, a pre-T_g exotherm was observed to develop with inelastic strain over a wide range of temperature. The pre-T_g exotherm was found to evolve until essentially reaching a steady-state profile at approximately −25% strain. This evolution coincided with the strain-softening phenomenon observed in the corresponding stress-strain results. A pre-T_g exotherm was also found to evolve with straining of the quenched material. Furthermore, the steady-state exotherms of the quenched and annealed materials were found to be nearly identical, as were their corresponding flow stress values after strain softening.

Finally, a second, post-T_g exotherm was found to develop with further straining beyond strains of −25%. This exotherm was found to increase with inelastic strain and coincided with the occurrence of strain hardening (due to chain orientation) in the materials.

The presence of two distinct and separately evolving exotherms in the inelastically deformed polymers indicates the existence of two separate deformation resistances in glassy polymers, one related to the initial yield and strain-softening behaviour, and the other to the orientation-induced strain hardening of the material. The observation that the pre-T_g exotherm is spread over a wide temperature range reflects the distributed nature of the structural state and may be quantified using a distribution in activation energy for the local rearrangements. The results therefore provide valuable information about the processes that must be accounted for in the development of accurate constitutive models of mechanical behaviour.     

Electric and magnetic properties of lanthanum barium cobaltite

The cubic Ba_0.5La_0.5CoO_3-δ was synthesized using solid state reaction. The structural properties were determined by the simultaneous refinement of Synchrotron Powder X-ray Diffraction and Neutron Powder Diffraction data. Iodometric titration was used to examine the oxygen stoichiometry and average cobalt oxidation state. Low-temperature magnetic studies show soft ferromagnetic character of fully oxidized material, with θ_P = 198(3) K and µ_eff = 2.11(2) µ_B. Electric measurements show the thermally activated nature of conductivity at low temperatures, whereas, due to the variable oxidation and spin state of cobalt, a single charge transport mechanism cannot be distinguished. Around room temperature, a wide transition from thermally activated conductivity to semi-metallic behavior is observed. Under the inert atmosphere, the oxygen content lowers and the cation ordering takes place, leading to coexistence of two, ordered and disordered, phases. As a result of this change, thermally activated conductivity is observed also at high temperatures in inert atmosphere.     

A state variable model for high strength polymers

Displacement controlled experiments on nylon 66, poly(etherether ketone), and poly(ether imide) at room temperature suggest that nonlinear elastcity is not a good model for these polymers. Rather, qualitative evidence is presented that a state variable model shows promise. In this model, the rate of deformation is the sum of the elastic and the inelastic rates of deformation. The elastic rate of deformation is given by an objective formulation of Hooke's law, and the inelastic deformation is an increasing function of the overstress, the difference between the Cauchy stress and the equilibrium stress. The equilibrium stress is a state variable, and represents the stress that can be sustained at rest following deformation. Load controlled tests, intended to verify or falsify the model, show that the creep rate at the same stress level can be different on loading and unloading, and that the creep rate need not increase with an increase in creep stress level. These anomalous results can easily be explained by the introduction of the overstress concept, and by proper evolution of the equilibrium stress. They confirm the usefulness of the overstress concept for the modeling of these polymers.     

Tensile mechanical properties and constitutive model for HTPB propellant at low temperature and high strain rate

To investigate the mechanical properties and fracture mechanisms of hydroxyl‐terminated polybutadiene (HTPB) propellant at low temperature and high strain rate, uniaxial tensile tests were conducted over the range of temperatures 233 to 298 K and strain rates 0.4 to 14.14 s^?1 using an INSTRON testing machine, and scanning electron microscope (SEM) was employed to observe the tensile fracture surfaces. The experimental results indicate that the deformation properties of HTPB propellant are remarkably influenced by temperature and strain rate. The characteristics of stress–strain curves at low temperatures are different from that at room temperature, and the effects of temperature and strain rate on the mechanical properties are closely related to the changes of properties and the fracture mechanisms of HTPB propellant. The dominating fracture mechanism depends much on the temperature and changes from the dewetting and matrix tearing at room temperature to the particle brittle fracture at low temperature, and the effect of strain rate only alters the mechanism in a quantitative manner. Finally, a nonlinear viscoelastic constitutive model incorporating the damage evolution and the effects of temperature and strain rate was developed to describe the stress responses of this propellant under the test conditions. During this process, the Schapery‐type constitutive theories were applied and one damage variable was considered to establish the damage evolution function. The overlap between experimental results and predicted results are generally good, which confirms that the developed constitutive model is valid, however, further researches should be done due to some drawbacks in describing the deformation behaviors at very large strain. © 2015 Wiley Periodicals, Inc. J. Appl. Polym. Sci. 2015 , 132, 42104.     

Attempt to correlate the yield processes above and below the glass transition in glassy polymers

This paper is concerned with a model which attempts to describe quantitatively, by the same elementary process, the yield behaviour above and below T_g, as well as the effect of annealing on the yield stress. This model links together theories we have previously proposed and relies on the following main assumptions: the deformation processes imply the cooperation of n activated segments and that the free energy increase of an activated segment depends on the structural state of the polymer. A satisfactory agreement is found with yield stress data on polycarbonate (PC), over a very large range of temperatures and strain rates. The correlation between the yield stress and the annealing treatment is also reasonable.     

The role of molecular networks and thermally activated processes in the deformation behavior of polymers

The deformation behavior of three polymers, polyethylene terephthalate (PET), polymethylmethacrylate (PMMA), and linear polyethylene (LPE) is considered in terms of two key factors, the stretching of a molecular network and the influence of thermally activated processes. In PET the observation of a natural draw ratio leads to studies of shrinkage, shrinkage force, and optical birefringence to define the nature of the network. The network is further exemplified by measurements of the molecular reorientation in deformation bands, spectroscopic studies of molecular orientation in drawing, and the concept of a true stress-strain curve. Yield and plastic deformation are also to be considered as thermally activated processes, but it appears that a major part of the flow stress is associated with the stretching of the molecular network. In PMMA the concept of a true stress strain curve also appears to be valuable, but the possibility of network breakdown during deformation has to be admitted as an extra complexity. In LPE the concept of a molecular network embracing both crystalline and non-crystalline material is helpful in understanding the drawing behavior. There is also direct evidence for the existence of a network from measurements of shrinkage and shrinkage force, and the existence of a true-stress strain curve. However, the dominant contribution to the flow stress now appears to come from thermally activated processes, with a key contribution from a small activation volume process which is tentatively associated with slip in the crystalline regions.     

Viscoplastic deformation of an epoxy resin at elevated temperatures

The tensile behavior under monotonic loading and stress‐relaxation testing of an epoxy resin has been studied. Experimental data at various strain rates and three temperatures from ambient up to just below T_g were performed, to study the transition from the brittle behavior to a ductile and therefore viscoplastic one. Dynamic mechanical analysis was applied to study the glass transition region of the material. Furthermore, a three‐dimensional viscoplastic model was used to simulate the experimental results. This model incorporates all features of yield, strain softening, strain hardening, and rate/temperature dependence. The multiplicative decomposition of the deformation tensor into an elastic and viscoplastic part has also been applied, following the element arrangement in the mechanical model. A stress‐dependent viscosity was controlling the stress–strain material behavior, involving model parameters, calculated from the Eyring plots. A new equation for the evolution of the activation volume with deformation was proposed, based on a probability density function. The model capability was further verified by applying the same set of parameters to predict with a good accuracy the stress‐relaxation data as well. © 2006 Wiley Periodicals, Inc. J Appl Polym Sci 101: 2027–2033, 2006     

Effect of microstructure on load-carrying and energy-dissipation capacities of UHPC

The load-carrying and energy dissipation capacities of ultra-high performance concrete (UHPC) under dynamic loading are evaluated in relation to microstructure composition at strain rates on the order of 10⁵ s^− 1 and pressures of up to 10 GPa. Analysis focuses on deformation and failure mechanisms at the mesostructural level. A cohesive finite element framework that allows explicit account of constituent phases, interfaces, and fracture is used. Three modes of energy dissipation are tracked, i.e., inelastic deformation, distributed cracking, and interfacial friction. Simulations are carried out over a range of volume fractions of constituent phases. Results show that (1) volume fractions of the constituents have more influence on the energy-dissipation than load-carrying capacity, (2) inelastic deformation is the source of over 70% of the energy dissipation, and (3) the presence of porosity changes the role of fibers in the dissipation process. Microstructure–behavior relations are established to facilitate materials design for target-specific applications.     

Modeling the uniaxial rate and temperature dependent behavior of amorphous and semicrystalline polymers

Strain rate and temperature dependent constitutive equations are proposed for polymer materials based on existing isotropic formulations of viscoplasticity. The proposed formulations are capable of simulating some of the important features of deformation behavior of amorphous and semicrystalline polymers. The materials model is based on the assumption that the evolution of flow stress is dependent on the rate of deformation, temperature, and an appropriate set of internal variables. The proposed theory is capable of modeling yielding, strain softening, and the orientation hardening exhibited by amorphous polymers. It is also possible to model the initial viscoplastic and subsequent nonlinear hardening behavior shown by semicrystalline polymers at large strains. Uniaxial tensile tests with uniform and hourglass specimens are made at temperatures ranging from 23 to 100°C and under various crosshead speeds. Both amorphous polycarbonate and semicrystalline polypropylene sheet materials are tested to characterize the stress and strain behavior of these materials and to determine their appropriate material constants. Load relaxation experiments are also conducted to obtain the necessary material constants describing the rate and temperature dependent flow stress behavior of polypropylene. Simulation results compare favorably against experimental data for these polymer materials.     

In-Plane Mechanical Properties of Several Ceramic-Matrix Composites

An attempt has been made to assess the generalized in-plane inelastic deformation and rupture properties of typical laminated or woven ceramic-matrix composites. The assessment is made by first identifying two principal classes of behavior. These classes are distinguished by the ratio of the elastic properties of the fibers to those of the matrix, which determines the mechanisms of deformation and rupture. These mechanisms, in turn, control the magnitude and orientation sensitivity of the stress/strain curves. Assessment of the inelastic deformations is achieved by first establishing the evolution of matrix cracks and their influence on the elastic moduli. Subsequent evaluation is made by using constituent properties, particularly the interface debonding and sliding resistances in the presence of matrix cracks. This is achieved by analyses of hysteresis loops, using a matrix cracking model. This model provides a representation of the influence of load direction on the interface responses and the inelastic strains. The ultimate strength is controlled by two mechanisms. It is fiber-controlled in 0/90 tension but becomes matrix controlled in ±45° tension. A model characterizing this mechanism change has yet to be devised.     

Mechanical Behavior of Samhire

The present state of the knowledge of the mechanical behavior of sapphire is reviewed. Sapphire deforms plastically at temperatures above 900°C, the most common mode of deformation being slip on the basal plane in the 〈11     0〉 direction. Under certain conditions, however, slip may occur on prism planes or twinning may occur. A yield point is often observed, which appears to be related to the multiplication of dislocations by a mechanism controlled by the motion of dislocations through the lattice, rather than by the tearing of dislocations from an impurity (or defect) atmosphere. The dynamics of yielding and flow is similar and can be expressed by either of two thermally activated equations. In one, the effect of stress is principally on the pre-exponential factor; in the other, its effect is principally on the activation energy. There are insufficient data to permit a positive decision between the two, or to positively identify the rate-controlling dislocation mechanism. For 60°-oriented crystals fracture generally occurs on a plane approximately normal to the tensile stress and the fracture surface is conchoidal. In the range 1100° to 1500°C, the tensile fracture stress decreases with increase in plastic strain, independent of temperature and strain rate. The mechanism of failure in this case seems to be the interaction of edge dislocations with pre-existing cracks.     

Effect of annealing time and molecular weight on melt memory of random ethylene 1‐butene copolymers

The effects of annealing time and molecular weight on the strong melt memory effect observed in random ethylene 1‐alkene copolymers are analyzed in a series of model ethylene 1‐butene copolymers with 2.2 mol% branches. Melt memory is associated with molten clusters of ethylene sequences from the initial crystals that remain in close proximity and are unable to diffuse quickly to the randomized melt state, thus increasing the recrystallization rate. Melt memory persists even for greater than 1000 min annealing indicating a long‐lived nature of the clusters that only fully dissolve at melt temperatures above a critical value (>160 °C). Below the critical melt temperature, molecular weight and annealing temperature have a strong influence on the slow kinetics of melt memory. For the copolymers analyzed, slow dissolution of clusters is experimentally observed only for M_w < 50 000 g mol^?1. More stable clusters that survive higher annealing temperatures display slower dissolution rates than clusters remaining at lower temperatures. The threshold crystallinity level to enable melt memory (X_c,threshold) decreases with increasing molecular weight and decreasing annealing temperature similarly to the variation of the chain diffusivity in the melt. The process leading to melt memory is thermally activated as the variation of X_c,threshold with temperature follows Arrhenius behavior with high activation energy (ca 108 kJ mol^?1) that is independent of molecular weight. © 2018 Society of Chemical Industry     

Constitutive equations in nonlinear viscoelasticity of glassy polymers based on the concept of traps

Constitutive equations are derived for the nonlinear viscoelastic response of amorphous polymers. The model treats a glassy polymer as an ensemble of independent relaxing regions that randomly hop in their cages being thermally activated. Rearrangement occurs when a flow unit reaches some liquid‐like state. Stress‐strain relations are verified using experimental data in tensile relaxation tests for polyester resins with two types of flexibilizers. Fair agreement is demonstrated between observations and results of numerical simulation.     

The Trapping Concept in Nonlinear Viscoelasticity of Amorphous Glassy Polymers

Abstract

Nonlinear stress - strain relations are derived for the viscoelastic behavior of glassy polymers. An amorphous medium is treated as an ensemble of cooperatively rearranging regions (flow units). Any unit is thought of as a point in the phase space which hops (being thermally activated) to higher energy levels in its potential well on the energy landscape. The viscoelastic behavior of a polymer is modeled as a sequence of rearrangement events occurring at random times when relaxing regions reach (in hops) some liquid-like level. We assume that external loads affect the position of the liquid-like state with respect to the energy landscape, and the descent of the reference energy level is proportional to the average mechanical energy of a flow unit. This hypothesis is verified by comparison of observations for polycarbonate in tensile relaxation tests with results of numerical simulation. Fair agreement is demonstrated between experimental data and their predictions.     

Rate‐dependent self‐healing behavior of an ethylene‐co‐methacrylic acid ionomer under high‐energy impact conditions

In this work, the mechanical and the self‐healing behaviors of an ethylene‐co‐methacrylic acid ionomer were investigated in different testing conditions. The self‐healing capability was explored by ballistic impact tests at low‐velocity, midvelocity, and hypervelocity bullet speed; different experimental conditions such as sample thickness and bullet diameter were examined; in all impact tests, spherical projectiles were used. These experiments, in particular those at low and midspeed, allowed to define a critical ratio between sample thickness and bullet diameter below which full repair was not observed. After ballistic damage, the healing efficiency was evaluated by applying a pressure gradient through tested samples. Subsequently, morphology analysis of the affected areas was made observing all tested samples by scanning electron microscope. This analysis revealed different characteristic features of the damaged zones affected at different projectile speed. Stress–strain curves in uniaxial tension performed at different temperatures and strain rates revealed yield strength and postyield behavior significantly affected by these two parameters. A rise of temperature during high strain rate tests in the viscoplastic deformation region was also detected. This behavior has a strong influence on the self‐repairing mechanism exhibited by the studied material during high‐energy impact tests. © 2013 Wiley Periodicals, Inc. J. Appl. Polym. Sci. 130: 1949–1958, 2013