Thermomechanical behavior of thermoset shape memory polymer programmed by cold-compression: Testing and constitutive modeling

Programming is a key process for thermally activated stress or strain recovery of shape memory polymers (SMPs). Typically, programming requires an initial heating above the glass transition temperature (T_g), subsequent cooling below T_g and removal of the applied load, in order to fix a temporary shape. This work adopted a new approach to program thermoset SMPs directly at temperatures well below T_g, which effectively simplified the shape fixing process. 1-D compression programming below T_g and free shape recovery of a thermoset SMP were experimentally investigated. Functional stability of the shape fixity under various environmental attacks was also experimentally evaluated. A mechanism-based thermoviscoelastic-thermoviscoplastic constitutive model incorporating structural and stress relaxation was then developed to predict the nonlinear shape memory behavior of the SMP trained below T_g. Comparison between the prediction and the experiment showed good agreement. The structure dependence of the thermomechanical behavior of the SMP was further discussed through a parametric study per the validated constitutive model. This study validates that programming by cold-compression is a viable alternative for thermally responsive thermoset SMPs.     

Finite deformation thermo-mechanical behavior of thermally induced shape memory polymers

Shape memory polymers (SMPs) are polymers that can demonstrate programmable shape memory effects. Typically, an SMP is pre-deformed from an initial shape to a deformed shape by applying a mechanical load at the temperature T_H>T_g. It will maintain this deformed shape after subsequently lowering the temperature to T_L<T_g and removing the externally mechanical load. The shape memory effect is activated by increasing the temperature to T_D>T_g, where the initial shape is recovered. In this paper, the finite deformation thermo-mechanical behaviors of amorphous SMPs are experimentally investigated. Based on the experimental observations and an understanding of the underlying physical mechanism of the shape memory behavior, a three-dimensional (3D) constitutive model is developed to describe the finite deformation thermo-mechanical response of SMPs. The model in this paper has been implemented into an ABAQUS user material subroutine (UMAT) for finite element analysis, and numerical simulations of the thermo-mechanical experiments verify the efficiency of the model. This model will serve as a modeling tool for the design of more complicated SMP-based structures and devices.     

Testing thermodynamic constitutive equations for polymers by adiabatic deformation experiments

During adiabatic deformation experiments on polyisobutylene of various molecular weights and on polyvinylacetate, the temperature change was measured. The thermal effects occurring during the subsequent stress relaxation were also recorded. From all data, the conclusion was drawn that the entropic elasticity theory is obeyed for temperatures sufficiently above the glass transition temperature. When the value of T_g is approached, some interesting energy effects become appreciable.     

Thermomechanics of shape memory polymers: Uniaxial experiments and constitutive modeling

Shape memory polymers (SMPs) can retain a temporary shape after pre-deformation at an elevated temperature and subsequent cooling to a lower temperature. When reheated, the original shape can be recovered. Relatively little work in the literature has addressed the constitutive modeling of the unique thermomechanical coupling in SMPs. Constitutive models are critical for predicting the deformation and recovery of SMPs under a range of different constraints. In this study, the thermomechanics of shape storage and recovery of an epoxy resin is systematically investigated for small strains (within ±10%) in uniaxial tension and uniaxial compression. After initial pre-deformation at a high temperature, the strain is held constant for shape storage while the stress evolution is monitored. Three cases of heated recovery are selected: unconstrained free strain recovery, stress recovery under full constraint at the pre-deformation strain level (no low temperature unloading), and stress recovery under full constraint at a strain level fixed at a low temperature (low temperature unloading). The free strain recovery results indicate that the polymer can fully recover the original shape when reheated above its glass transition temperature (T_g). Due to the high stiffness in the glassy state (T < T_g), the evolution of the stress under strain constraint is strongly influenced by thermal expansion of the polymer. The relationship between the final recoverable stress and strain is governed by the stress–strain response of the polymer above T_g. Based on the experimental results and the molecular mechanism of shape memory, a three-dimensional small-strain internal state variable constitutive model is developed. The model quantifies the storage and release of the entropic deformation during thermomechanical processes. The fraction of the material freezing a temporary entropy state is a function of temperature, which can be determined by fitting the free strain recovery response. A free energy function for the model is formulated and thermodynamic consistency is ensured. The model can predict the stress evolution of the uniaxial experimental results. The model captures differences in the tensile and compressive recovery responses caused by thermal expansion. The model is used to explore strain and stress recovery responses under various flexible external constraints that would be encountered in applications of SMPs.     

Viscosity and dynamics of nanorod (carbon nanotubes, cellulose whiskers, stiff polymers and polymer fibers) suspensions

The zero shear viscosity and the dynamic behaviors of different nanorod dispersions (carbon nanotubes (CNTs), cellulose whiskers, polymer nanofibers, crosslinked polymer nanofibers, and stiff polymers such as poly(γ-benzyl-α-l-glutamate) (PBLG)) were compared and discussed from literature data. Their Brownian dynamic behaviors have always been discussed in the frame of the Doi–Edwards theory. In agreement with this theory, the straight rigid rods (CNTs, cellulose whisker, polymer nanofibers) obey a master curve in the reduced viscosity (or rotary diffusivity) c power laws on viscosity (η ₀ ∝ φ ³) and diffusivity (D _r ∝ ? ^?2). On the contrary, stiff polymer chains and crosslinked polymer fibers at temperature above T _g exhibit different and two distinct dynamic behaviors. Despite their deviation from the ideal rigidity, surprisingly it can be noted that stiff polymers such as PBLG have been extremely used in the literature to verify the Doi–Edwards theory. Finally, flexible crosslinked chains at T > T _g , do not obey the Doi–Edwards theory, and their dynamics are close to the physics of polymer solutions in terms of power laws.     

Longitudinal volume viscosity of poly (vinyl chloride)

The volume flow of poly (vinyl chloride) ( = 45,000,T _g = 350 K) has been measured in an Instron Capillary Rheometer.The elastic modulus in longitudinal compression, the longitudinal volume viscosity and initial longitudinal volume viscosity, and retardation times were determined at temperatures both below (324 – 343 K) and above (403 – 453 K) the glass transition temperatureT _g , and at compression rates between approximately 10^–5 and 200 · 10^–5 s^–1.An increase in the longitudinal volume viscosity was observed for decreases in the volume deformation, increases in the compression rate and increases in temperature.T _g decreased at 0.16 K/MPa. The volume flow activation energy was found to be equal to that for shear flow with a constant value of 91.37 kJ/mol.     

Modified correlation for minimum fluidization velocity of low-density particles in inverse liquid–solid fluidized beds

The minimum fluidization velocity (U_mf) is a key parameter for the scale-up of inverse liquid–solid fluidized beds. Theoretical predictions using common correlations were compared against experimental minimum fluidization velocity measurements of low density (28–638 kg/m³), 0.80–1.13 mm Styrofoam particles in a fluidized bed with a height of 4.5 m and 0.2 m diameter. The average absolute relative deviation for the predicted minimum fluidization velocity for particles below 300 kg/m³ was above 40% using the studied common correlations. A modified Wen and Yu correlation was thus proposed based on novel and past measurements with low-density and small-diameter particles, expanding the range for predicting U_mf. The new correlation predicted U_mf with deviations below 15% for ST028, ST122 and ST300. This modified correlation also improved U_mf predictions for comparable particles from a previous study, demonstrating its validity for a larger range of low-density particles.     

Scaling relations for elongational flow of polystyrene melts and concentrated solutions of polystyrene in oligomeric styrene

A consistent model of the rheology of polymer melts and concentrated solutions is presented, based on the idea that the pressures exerted by a polymer chain on the walls of an anisotropic confinement are anisotropic (Doi and Edwards. The Theory of Polymer Dynamics, Oxford University Press, 1986). In a tube model with variable tube diameter, chain stretch and tube diameter reduction are related, and at deformation rates larger than the inverse Rouse time τ _R, the chain is stretched and its confining tube becomes increasingly anisotropic. Tube diameter reduction leads to an interchain pressure in the lateral direction of the tube (Marrucci and Ianniruberto. Macromolecules 37:3934-3942, 2004). Chain stretch is balanced by interchain tube pressure in the lateral direction, which is proportional to the third power of stretch, and by a spring force in the longitudinal direction of the tube, which is linear in stretch. Analyzing elongational viscosity data of Huang et al. (Macromolecules 46:5026-5035, 2013a; ACS Macro Letters 2:741-744, 2013b) shows that dilution of polystyrene by oligomeric styrene does not change the relative interchain tube pressure. Based on this extended interchain pressure concept, scaling relations for linear viscoelasticity and elongational viscosity of polystyrene melts and concentrated solutions of polystyrene in oligomeric styrene are presented based exclusively on the relaxation modulus of a reference polymer melt, the volume fraction of polymer in the solution, and the time-molar-mass shift as well as the time-temperature shift caused by the reduction of the glass transition temperature T _g of the polymer in a solution relative to T _g of the melt.     

Pressure dependence of glass transition temperature in polymers

The pressure dependencedT _g /dP of glass transition temperatureT _g has received considerable interest due to its connection with solid state thermodynamic properties and theories of glass transition. Free volume considerations (1, 2) led to an estimate of the pressure effect onT _g , showing thatdT _g /dP had to depend on thermal expansion and compressibility changes atT _g through the equation: [1] $$\frac{{dT_g }}{{dP}} = \frac{{\Delta \beta }}{{\Delta \alpha }}$$ whereΔβ=β _e ?β _g andΔα=α _e ?α _g Later work (3, 4, 5, 6) has shown that eq. [1] is not verified by experimental facts, the ratioΔβ/Δα being much larger than (dT _g /dP) exp. Recent analysis of the properties of glasses obtained under different pressures have complicated the situation, showing that the experimental value ofdT _g /dP depends, of course, on the polymer usedbut also on the experimental procedure used in its determination. Since it is obvious that in order to measure anyΔT _g -value we need to operate on at leasttwo glasses, these should be identical in all properties which could influenceT _g except pressure. Any difference in morphology,which could lead to a change in T _g at constant pressure, should therefore be avoided in order to get a sound value for the pure pressure effectdT _g /dP. To reveal this effect, we have performed (7)dT _g /dP determinations on two polymers, polyvinylacetate (PVAC) and polyvinylchloride (PVC), following three different procedures:

1. Measurement of the changeΔT _g induced by application of a pressure incrementΔP on the liquid polymer (T>T _g ). This is the procedure normally used; the liquid is cooled down at a fixed rate of temperature change (～5 °C/day) andT _g is dilatometrically recorded at 1 atmosphere. Then the polymer is taken again to the liquid state, pressure ΔP is applied and, at the same rate, the system is cooled down isobarically; the newT _g is recorded anddT _g /dP calculated.
2. Measurement of the change ΔT_g induced by application of a pressure increment ΔP on the glassy polymer (T _g ). Once determinedT _g at 1 atmosphere, pressureΔP is applied on the glass, time is given to the system to equilibrate; then the glass is heated isobarically. Intersection of the glassy line to the liquid line in a volume/temperature plot gives the newT _g and therefore allows the calculation ofdT _g /dP.
3. Measurement ofΔT _g during the heating of a glass along an isochor (5, 8). Here the polymer glass is heated at constant volume, by application of an increasing pressure at increasing temperatures given by(?P/?T) _v . By repeating this procedure two times, starting from two different specific volumes of the glass, two values ofT _g at different pressures can be recorded anddT _g /dP calculated.

   Table 1 shows the result of this work     

   10.

   Entropy productions in granular materials     

   Qicheng Sun  Shixiong Song  Feng Jin  Yimin Jiang 《力学快报》2012,2(2):021002

   Granular materials display more abundant dissipation phenomena than ordinary materials. In this paper, a brief energy flow path with irreversible processes is illustrated, where the concept of granular temperature T_g, initially proposed for dilute systems, is extended to dense systems in order to quantify disordered force chain configurations. Additionally, we develop the concept of conjugate granular entropy s_g and its production equation. Our analyses find out that the granular entropy significantly undermined the elastic contact between particles, seriously affecting the transport coefficients in granular materials and creating new transport processes.     

   11.

   Influence of Thermally Induced Chemorheological Changes on the Inflation of Spherical Elastomeric Membranes     

   Alan Wineman  John Shaw 《Journal of Elasticity》2005,80(1-3):73-95

   When an elastomeric material is deformed and subjected to temperatures above some chemorheological value T _cr (near 100°C for natural rubber), its macromolecular structure undergoes time and temperature dependent chemical changes. The process continues until the temperature decreases below T _cr. Compared to the virgin material, the new material system has modified properties (often a reduced stiffness) and permanent set on removal of the applied load. A recently proposed constitutive theory is used to study the influence of chemorheological changes on the inflation of an initially isotropic spherical rubber membrane. The membrane is inflated while at a temperature below T _cr. We then look at the pressure response assuming the sphere's radius is held fixed while the temperature is increased above T _cr for a period of time and then returned to its original value. The inflation pressure during this process is expressed in terms of the temperature, representing entropic stiffening of the elastomer, and a time dependent property that represents the kinetics of the chemorheological change in the elastomer. When the membrane has been returned to its original temperature, it is shown to have a permanent set and a modified pressure-inflated radius relation. Their dependence on the initial inflated radius, material properties and kinetics of chemorheological change is studied when the underlying elastomeric networks are neo-Hookean or Mooney–Rivlin.     

   12.

   The effect of inhomogeneous plastic deformation on the ductility and fracture behavior of age hardenable aluminum alloys     

   《International Journal of Plasticity》2005,21(6):1097-1118

   The role of alloy composition, grain structure, precipitate microstructure, and precipitate dislocation interactions on the plastic deformation characteristics and the resulting fracture behavior of two isotropic Al–Li–Cu–X alloys designated AF/C-458 (1.8 w/o Li) and AF/C-489 (2.1 w/o Li) was examined. Inhomogeneous deformation due to strain localization from the shearing of the δ′ (Al₃Li), θ′ (Al₂Cu), and T₁ (Al₂CuLi) precipitates lead to fine and coarse planar slip for the AF/C-458 and AF/C-489 alloys, respectively. The intensity of this planar slip was predicted through slip intensity calculations using precipitate density measurements, dislocation particle interactions, and grain boundary misorientation-slip continuity statistics. The slip intensity predictions were corroborated through atomic force microscopy (AFM) measured slip height offsets on the polished surface of single aged and 2% plastically strained tensile samples. Our results suggest that the low ductility of AF/C-489 in comparison to AF/C-458 is primarily due to the much larger slip lengths, i.e. grain size, which increased the strain localization and stress concentrations on grain boundaries, thus promoting low-energy intergranular fracture.     

   13.

   Compressive creep of IM7/K3B composite and the effects of physical aging on viscoelastic behavior     

   D. R. Veazie  T. S. Gates 《Experimental Mechanics》1997,37(1):62-68

        

   14.

   A Peierls criterion for the onset of deformation twinning at a crack tip     

   E.B. Tadmor  S. Hai 《Journal of the mechanics and physics of solids》2003,51(5):765-793

   A criterion for the onset of deformation twinning (DT) is derived within the Peierls framework for dislocation emission from a crack tip due to Rice (J. Mech. Phys. Solids 40(2) (1992) 239). The critical stress intensity factor (SIF) is obtained for nucleation of a two-layer microtwin, which is taken to be a precursor to DT. The nucleation of the microtwin is controlled by the unstable twinning energyγ_ut, a new material parameter identified in the analysis. γ_ut plays the same role for DT as γ_us, the unstable stacking energy introduced by Rice, plays for dislocation emission. The competition between dislocation emission and DT at the crack tip is quantified by the twinning tendencyT defined as the ratio of the critical SIFs for dislocation nucleation and microtwin formation. DT is predicted when T>1 and dislocation emission when T<1. For the case where the external loading is proportional to a single load parameter, T is proportional to . The predictions of the criterion are compared with atomistic simulations for aluminum of Hai and Tadmor (Acta Mater. 51 (2003) 117) for a number of different crack configurations and loading modes. The criterion is found to be qualitatively exact for all cases, predicting the correct deformation mode and activated slip system. Quantitatively, the accuracy of the predicted nucleation loads varies from 5% to 56%. The sources of error are known and may be reduced by appropriate extensions to the model.     

   15.

   Combined deformation- and temperature-induced scission in a rubber cylinder in torsion     

   Alan Wineman  John Shaw 《International Journal of Non》2007,42(2):330-335

   When an elastomeric material is deformed and subjected to temperatures above some characteristic value T_cr (near for natural rubber), it undergoes time and temperature dependent chemical changes consisting of scission and crosslinking of its macromolecular structure. The process continues until the temperature decreases below T_cr. Experiments carried out in uniaxial extension have shown that the chemical changes are independent of stretch ratio within moderate stretches. It is reasonable to expect that the chemical changes would be affected by sufficiently large deformations, an interaction referred to as ‘mechanochemistry’. A kinetic theory of the breakdown of solids by Zhurkov [Kinetic concept of strength of solids, Int. J. Fract. Mech. 1 (1965) 311-323. [15]] attributes this interaction to the lowering of activation energy by mechanical work.In a recent constitutive theory, an expression was developed that relates the chemical kinetics of scission of the original elastomeric network to time, temperature and activation energy. The kinetic theory of Zhurkov suggests a method for modifying this expression to account for the influence of deformation. This is explored in the case of simple shear deformations, such as those occurring during torsion of elastomeric cylinders held at fixed length. Using the approach of Penn and Kearsley [The scaling law for finite torsion of elastic cylinders, Trans. Soc. Rheology 20 (1976) 227-238. [16]], it is shown that experiments in torsion can be used to determine the influence of shear deformations on the chemical kinetics of scission.     

   16.

   An inversion method for identification of elastoplastic properties of a beam from torsional experiment     

   Alemdar Hasanov  Salih Tatar 《International Journal of Non》2010,45(5):562-571

   A new method of determining elastoplastic properties of a beam from an experimentally given value T?T(φ) of torque (or torsional rigidity), during the quasistatic process of torsion, given by the angle of twist φ∈[φ_*,φ^*], is proposed. The mathematical model leads to the inverse problem of determining the unknown coefficient g=g(ξ²), ξ?|∇u|, of the non-linear differential equation −∇(g(|∇u|²)∇u)=2φ, x∈Ω⊂R². The inversion method is based on the parametrization of the unknown coefficient, according to the discrete values of the gradient ξ?|∇u|. Within the range of J₂-deformation theory, it is shown that the considered inverse coefficient problem is an ill-conditioned one. A numerical reconstruction algorithm based on parametrization of the unknown coefficient g=g(ξ²), with optimal selection of the experimentally given data T_m?T(φ_m), is proposed as a new regularization scheme for the considered inverse problem. Numerical results with noise free and noisy data illustrate applicability and high accuracy of the proposed method.     

   17.

   Energy dissipation mechanisms in ductile fracture     

   Jeffrey W. Kysar 《Journal of the mechanics and physics of solids》2003,51(5):795-824

   The objective is to investigate energy dissipation mechanisms that operate at different length scales during fracture in ductile materials. A dimensional analysis is performed to identify the sets of dimensionless parameters which contribute to energy dissipation via dislocation-mediated plastic deformation at a crack tip. However, rather than using phenomenological variables such as yield stress and hardening modulus in the analysis, physical variables such as dislocation density, Burgers vector and Peierls stress are used. It is then shown via elementary arguments that the resulting dimensionless parameters can be interpreted in terms of competitions between various energy dissipation mechanisms at different length scales from the crack tip; the energy dissipations mechanisms are cleavage, crack tip dislocation nucleation and also dislocation nucleation from a Frank-Read source. Therefore, the material behavior is classified into three groups. The first two groups are the well-known intrinsic brittle and intrinsic ductile behavior. The third group is designated to be extrinsic ductile behavior for which Frank-Read dislocation nucleation is the initial energy dissipation mechanism. It is shown that a material is predicted to exhibit extrinsic ductility if the dimensionless parameter bρ_disl^1/2 (b is Burgers vector, ρ_disl is dislocation density) is within a certain range defined by other dimensionless parameters, irrespective of the competition between cleavage and crack tip dislocation nucleation. The predictions compare favorably to the documented behavior of a number of different classes of materials.     

   18.

   Influence of thermally induced chemorheological changes on the torsion of elastomeric circular cylinders     

   Alan Wineman  John Shaw 《Continuum Mechanics and Thermodynamics》2006,17(7):477-492

   When an elastomeric material is deformed and subjected to temperatures above some characteristic value T _cr (near 100^∘C for natural rubber), its macromolecular structure undergoes time and temperature-dependent chemical changes. The process continues until the temperature decreases below T _cr. Compared to the virgin material, the new material system has modified properties (reduced stiffness) and permanent set on removal of the applied load.A new constitutive theory is used to study the influence of the changes of macromolecular structure on the torsion of an initially homogenous elastomeric cylinder. The cylinder is held at its initial length and given a fixed twist while at a temperature below T _cr. The twist is then held fixed and the temperature of the outer radial surface is increased above T _cr for a period of time and then returned to its original value. Assuming radial heat conduction, each material element undergoes a different chemical change. After enough time has elapsed such that the temperature field is again uniform and at its initial value, the cylinder properties are now inhomogeneous. Expressions for the time variation of the twisting moment and axial force are determined, and related to assumptions about material properties. Assuming the elastomeric networks to act as Mooney-Rivlin materials, expressions are developed for the permanent twist on release of torque, residual stress, and the new torsional stiffness in terms of the kinetics of the chemical changes.     

   19.

   Modeling of ductile fracture: Significance of void coalescence     

   《International Journal of Solids and Structures》2006,43(20):6277-6293

   In this paper void coalescence is regarded as the result of localization of plastic flow between enlarged voids. We obtain the failure criterion for a representative material volume (RMV) in terms of the macroscopic equivalent strain (E_c) as a function of the stress triaxiality parameter (T) and the Lode angle (θ) by conducting systematic finite element analyses of the void-containing RMV subjected to different macroscopic stress states. A series of parameter studies are conducted to examine the effects of the initial shape and volume fraction of the primary void and nucleation, growth, and coalescence of secondary voids on the predicted failure surface E_c(T, θ). As an application, a numerical approach is proposed to predict ductile crack growth in thin panels of a 2024-T3 aluminum alloy, where a porous plasticity model is used to describe the void growth process and the expression for E_c is calibrated using experimental data. The calibrated computational model is applied to predict crack extension in fracture specimens having various initial crack configurations and the numerical predictions agree very well with experimental measurements.     

   20.

   Scalar Dissipation Rate Transport in the Context of Large Eddy Simulations for Turbulent Premixed Flames with Non-Unity Lewis Number     

   Y. Gao  N. Chakraborty  N. Swaminathan 《Flow, Turbulence and Combustion》2014,93(3):461-486

   The effects of global Lewis number Le on the statistical behaviour of the unclosed terms in the transport equation of the Favre-filtered scalar dissipation rate (SDR) Ñ _c have been analysed using a Direct Numerical Simulation (DNS) database of freely propagating statistically planer turbulent premixed flames with Le ranging from 0.34 to 1.2. The DNS data has been explicitly filtered to analyse the statistical behaviour of the unclosed terms in the SDR transport equation arising from turbulent transport T ₁, density variation due to heat release T ₂, scalar-turbulence interaction T ₃, reaction rate gradient T ₄, molecular dissipation (?D ₂) and diffusivity gradients f(D) in the context of Large Eddy Simulations (LES). It Le has significant effects on the magnitudes of T ₁, T ₂, T ₃, T ₄, (?D ₂) and f(D). Moreover, both qualitative and quantitative behaviours of the unclosed terms T ₁, T ₂, T ₃, T ₄, (?D ₂) and f(D) are found to be significantly affected by the LES filter width Δ, which have been explained based on a detailed scaling analysis. Both scaling analysis and DNS data suggest that T ₂, T ₃, T ₄, (?D ₂) and f(D) remain leading order contributors to the SDR \(\tilde {{N}}_{c} \) transport for LES. The scaling estimates of leading order contributors to the SDR \(\tilde {{N}}_{c} \) transport has been utilised to discuss the possibility of extending an existing SDR model for Reynolds Averaged Navier Stokes (RANS) simulation for SDR \(\tilde {{N}}_{c} \) closure in the context of LES of turbulent premixed combustion.     

Entropy productions in granular materials

Granular materials display more abundant dissipation phenomena than ordinary materials. In this paper, a brief energy flow path with irreversible processes is illustrated, where the concept of granular temperature T_g, initially proposed for dilute systems, is extended to dense systems in order to quantify disordered force chain configurations. Additionally, we develop the concept of conjugate granular entropy s_g and its production equation. Our analyses find out that the granular entropy significantly undermined the elastic contact between particles, seriously affecting the transport coefficients in granular materials and creating new transport processes.     

Influence of Thermally Induced Chemorheological Changes on the Inflation of Spherical Elastomeric Membranes

When an elastomeric material is deformed and subjected to temperatures above some chemorheological value T _cr (near 100°C for natural rubber), its macromolecular structure undergoes time and temperature dependent chemical changes. The process continues until the temperature decreases below T _cr. Compared to the virgin material, the new material system has modified properties (often a reduced stiffness) and permanent set on removal of the applied load. A recently proposed constitutive theory is used to study the influence of chemorheological changes on the inflation of an initially isotropic spherical rubber membrane. The membrane is inflated while at a temperature below T _cr. We then look at the pressure response assuming the sphere's radius is held fixed while the temperature is increased above T _cr for a period of time and then returned to its original value. The inflation pressure during this process is expressed in terms of the temperature, representing entropic stiffening of the elastomer, and a time dependent property that represents the kinetics of the chemorheological change in the elastomer. When the membrane has been returned to its original temperature, it is shown to have a permanent set and a modified pressure-inflated radius relation. Their dependence on the initial inflated radius, material properties and kinetics of chemorheological change is studied when the underlying elastomeric networks are neo-Hookean or Mooney–Rivlin.     

The effect of inhomogeneous plastic deformation on the ductility and fracture behavior of age hardenable aluminum alloys

The role of alloy composition, grain structure, precipitate microstructure, and precipitate dislocation interactions on the plastic deformation characteristics and the resulting fracture behavior of two isotropic Al–Li–Cu–X alloys designated AF/C-458 (1.8 w/o Li) and AF/C-489 (2.1 w/o Li) was examined. Inhomogeneous deformation due to strain localization from the shearing of the δ′ (Al₃Li), θ′ (Al₂Cu), and T₁ (Al₂CuLi) precipitates lead to fine and coarse planar slip for the AF/C-458 and AF/C-489 alloys, respectively. The intensity of this planar slip was predicted through slip intensity calculations using precipitate density measurements, dislocation particle interactions, and grain boundary misorientation-slip continuity statistics. The slip intensity predictions were corroborated through atomic force microscopy (AFM) measured slip height offsets on the polished surface of single aged and 2% plastically strained tensile samples. Our results suggest that the low ductility of AF/C-489 in comparison to AF/C-458 is primarily due to the much larger slip lengths, i.e. grain size, which increased the strain localization and stress concentrations on grain boundaries, thus promoting low-energy intergranular fracture.     

A Peierls criterion for the onset of deformation twinning at a crack tip

A criterion for the onset of deformation twinning (DT) is derived within the Peierls framework for dislocation emission from a crack tip due to Rice (J. Mech. Phys. Solids 40(2) (1992) 239). The critical stress intensity factor (SIF) is obtained for nucleation of a two-layer microtwin, which is taken to be a precursor to DT. The nucleation of the microtwin is controlled by the unstable twinning energyγ_ut, a new material parameter identified in the analysis. γ_ut plays the same role for DT as γ_us, the unstable stacking energy introduced by Rice, plays for dislocation emission. The competition between dislocation emission and DT at the crack tip is quantified by the twinning tendencyT defined as the ratio of the critical SIFs for dislocation nucleation and microtwin formation. DT is predicted when T>1 and dislocation emission when T<1. For the case where the external loading is proportional to a single load parameter, T is proportional to . The predictions of the criterion are compared with atomistic simulations for aluminum of Hai and Tadmor (Acta Mater. 51 (2003) 117) for a number of different crack configurations and loading modes. The criterion is found to be qualitatively exact for all cases, predicting the correct deformation mode and activated slip system. Quantitatively, the accuracy of the predicted nucleation loads varies from 5% to 56%. The sources of error are known and may be reduced by appropriate extensions to the model.     

Combined deformation- and temperature-induced scission in a rubber cylinder in torsion

When an elastomeric material is deformed and subjected to temperatures above some characteristic value T_cr (near for natural rubber), it undergoes time and temperature dependent chemical changes consisting of scission and crosslinking of its macromolecular structure. The process continues until the temperature decreases below T_cr. Experiments carried out in uniaxial extension have shown that the chemical changes are independent of stretch ratio within moderate stretches. It is reasonable to expect that the chemical changes would be affected by sufficiently large deformations, an interaction referred to as ‘mechanochemistry’. A kinetic theory of the breakdown of solids by Zhurkov [Kinetic concept of strength of solids, Int. J. Fract. Mech. 1 (1965) 311-323. [15]] attributes this interaction to the lowering of activation energy by mechanical work.In a recent constitutive theory, an expression was developed that relates the chemical kinetics of scission of the original elastomeric network to time, temperature and activation energy. The kinetic theory of Zhurkov suggests a method for modifying this expression to account for the influence of deformation. This is explored in the case of simple shear deformations, such as those occurring during torsion of elastomeric cylinders held at fixed length. Using the approach of Penn and Kearsley [The scaling law for finite torsion of elastic cylinders, Trans. Soc. Rheology 20 (1976) 227-238. [16]], it is shown that experiments in torsion can be used to determine the influence of shear deformations on the chemical kinetics of scission.     

An inversion method for identification of elastoplastic properties of a beam from torsional experiment

A new method of determining elastoplastic properties of a beam from an experimentally given value T?T(φ) of torque (or torsional rigidity), during the quasistatic process of torsion, given by the angle of twist φ∈[φ_*,φ^*], is proposed. The mathematical model leads to the inverse problem of determining the unknown coefficient g=g(ξ²), ξ?|∇u|, of the non-linear differential equation −∇(g(|∇u|²)∇u)=2φ, x∈Ω⊂R². The inversion method is based on the parametrization of the unknown coefficient, according to the discrete values of the gradient ξ?|∇u|. Within the range of J₂-deformation theory, it is shown that the considered inverse coefficient problem is an ill-conditioned one. A numerical reconstruction algorithm based on parametrization of the unknown coefficient g=g(ξ²), with optimal selection of the experimentally given data T_m?T(φ_m), is proposed as a new regularization scheme for the considered inverse problem. Numerical results with noise free and noisy data illustrate applicability and high accuracy of the proposed method.     

Energy dissipation mechanisms in ductile fracture

The objective is to investigate energy dissipation mechanisms that operate at different length scales during fracture in ductile materials. A dimensional analysis is performed to identify the sets of dimensionless parameters which contribute to energy dissipation via dislocation-mediated plastic deformation at a crack tip. However, rather than using phenomenological variables such as yield stress and hardening modulus in the analysis, physical variables such as dislocation density, Burgers vector and Peierls stress are used. It is then shown via elementary arguments that the resulting dimensionless parameters can be interpreted in terms of competitions between various energy dissipation mechanisms at different length scales from the crack tip; the energy dissipations mechanisms are cleavage, crack tip dislocation nucleation and also dislocation nucleation from a Frank-Read source. Therefore, the material behavior is classified into three groups. The first two groups are the well-known intrinsic brittle and intrinsic ductile behavior. The third group is designated to be extrinsic ductile behavior for which Frank-Read dislocation nucleation is the initial energy dissipation mechanism. It is shown that a material is predicted to exhibit extrinsic ductility if the dimensionless parameter bρ_disl^1/2 (b is Burgers vector, ρ_disl is dislocation density) is within a certain range defined by other dimensionless parameters, irrespective of the competition between cleavage and crack tip dislocation nucleation. The predictions compare favorably to the documented behavior of a number of different classes of materials.     

Influence of thermally induced chemorheological changes on the torsion of elastomeric circular cylinders

When an elastomeric material is deformed and subjected to temperatures above some characteristic value T _cr (near 100^∘C for natural rubber), its macromolecular structure undergoes time and temperature-dependent chemical changes. The process continues until the temperature decreases below T _cr. Compared to the virgin material, the new material system has modified properties (reduced stiffness) and permanent set on removal of the applied load.A new constitutive theory is used to study the influence of the changes of macromolecular structure on the torsion of an initially homogenous elastomeric cylinder. The cylinder is held at its initial length and given a fixed twist while at a temperature below T _cr. The twist is then held fixed and the temperature of the outer radial surface is increased above T _cr for a period of time and then returned to its original value. Assuming radial heat conduction, each material element undergoes a different chemical change. After enough time has elapsed such that the temperature field is again uniform and at its initial value, the cylinder properties are now inhomogeneous. Expressions for the time variation of the twisting moment and axial force are determined, and related to assumptions about material properties. Assuming the elastomeric networks to act as Mooney-Rivlin materials, expressions are developed for the permanent twist on release of torque, residual stress, and the new torsional stiffness in terms of the kinetics of the chemical changes.     

Modeling of ductile fracture: Significance of void coalescence

In this paper void coalescence is regarded as the result of localization of plastic flow between enlarged voids. We obtain the failure criterion for a representative material volume (RMV) in terms of the macroscopic equivalent strain (E_c) as a function of the stress triaxiality parameter (T) and the Lode angle (θ) by conducting systematic finite element analyses of the void-containing RMV subjected to different macroscopic stress states. A series of parameter studies are conducted to examine the effects of the initial shape and volume fraction of the primary void and nucleation, growth, and coalescence of secondary voids on the predicted failure surface E_c(T, θ). As an application, a numerical approach is proposed to predict ductile crack growth in thin panels of a 2024-T3 aluminum alloy, where a porous plasticity model is used to describe the void growth process and the expression for E_c is calibrated using experimental data. The calibrated computational model is applied to predict crack extension in fracture specimens having various initial crack configurations and the numerical predictions agree very well with experimental measurements.     

Scalar Dissipation Rate Transport in the Context of Large Eddy Simulations for Turbulent Premixed Flames with Non-Unity Lewis Number

The effects of global Lewis number Le on the statistical behaviour of the unclosed terms in the transport equation of the Favre-filtered scalar dissipation rate (SDR) Ñ _c have been analysed using a Direct Numerical Simulation (DNS) database of freely propagating statistically planer turbulent premixed flames with Le ranging from 0.34 to 1.2. The DNS data has been explicitly filtered to analyse the statistical behaviour of the unclosed terms in the SDR transport equation arising from turbulent transport T ₁, density variation due to heat release T ₂, scalar-turbulence interaction T ₃, reaction rate gradient T ₄, molecular dissipation (?D ₂) and diffusivity gradients f(D) in the context of Large Eddy Simulations (LES). It Le has significant effects on the magnitudes of T ₁, T ₂, T ₃, T ₄, (?D ₂) and f(D). Moreover, both qualitative and quantitative behaviours of the unclosed terms T ₁, T ₂, T ₃, T ₄, (?D ₂) and f(D) are found to be significantly affected by the LES filter width Δ, which have been explained based on a detailed scaling analysis. Both scaling analysis and DNS data suggest that T ₂, T ₃, T ₄, (?D ₂) and f(D) remain leading order contributors to the SDR \(\tilde {{N}}_{c} \) transport for LES. The scaling estimates of leading order contributors to the SDR \(\tilde {{N}}_{c} \) transport has been utilised to discuss the possibility of extending an existing SDR model for Reynolds Averaged Navier Stokes (RANS) simulation for SDR \(\tilde {{N}}_{c} \) closure in the context of LES of turbulent premixed combustion.