Recoverable Elastic Energy Research Articles

Mechanical Behavior of Shale at Different Strain Rates

The strain rate-dependent mechanical behavior of shale is characterized using triaxial compression tests under a constant confining pressure of 50 MPa and axial strain rates $$\dot{\varepsilon }_{1}$$ ranging from 5 × 10−6 s−1 to 1 × 10−3 s−1. This study is conducted on the Longmaxi shale from Dayou in China, which is predominantly composed of brittle minerals including quartz (55%), albite (15%) and cristobalite (3%). The experimental results show that higher axial loading strain rates $$\dot{\varepsilon }_{1}$$ lead to higher elastic modulus and higher peak shear strength, both following exponential relationships with $$\dot{\varepsilon }_{1}$$ . When $$\dot{\varepsilon }_{1} \le 1 \times 10^{ - 5} {\text{s}}^{ - 1}$$ , failure results in a single linear fracture, whereas a more complex multiple crisscrossing fracture network is formed when $$\dot{\varepsilon }_{1} \ge 1 \times 10^{ - 4} {\text{s}}^{ - 1}$$ . Failure in shale specimens can be described by a damage parameter $$D$$ , which is strongly affected by the axial strain $$\varepsilon_{{1{\text{s}}}}$$ . In addition, the strain rate $$\dot{\varepsilon }_{1}$$ had different effects on $$D$$ , which also depends on axial strain $$\varepsilon_{{1{\text{s}}}}$$ . Energy accumulation and dissipation are also closely related to $$\dot{\varepsilon }_{1}$$ with the total absorbed energy $$U_{\text{A}}$$ , the recoverable elastic strain energy $$U_{\text{A}}^{\text{e}}$$ and the dissipated energy $$U_{\text{A}}^{\text{d}}$$ at the peak stress increasing with $$\dot{\varepsilon }_{1}$$ . As for the total energy accumulation $$U_{\text{A}}$$ , the recoverable elastic energy $$U_{\text{A}}^{\text{e}}$$ decreases while the dissipated energy $$U_{\text{A}}^{\text{d}}$$ increases with increasing strain rate.

Co content effect on elastic strain limit in ZrCuNiAlCo bulk metallic glasses

The microstructures and mechanical properties of Zr64−xNi10Al7Cu19Cox (x=0–16at.%) bulk metallic glasses (BMGs) were investigated as a function of cobalt content. Due to negative mixing enthalpy between cobalt and zirconium, the atomic packing structure of studied BMGs changes with the addition of cobalt while the positive mixing enthalpy between cobalt and copper leads to phase separation and the formation of nanoglass with glassy grain sizes of about 5–10nm. With the unique topological structure, the stored recoverable elastic energy in these studied BMGs increases dramatically with the increasing cobalt content. The Zr55.7Ni10Al7Cu19Co8.3 BMG exhibits excellent mechanical properties at ambient temperature.

Molecular dynamics based study and characterization of deformation mechanisms near a crack in a crystalline material

Modeling crack propagation in crystalline materials is a challenging enterprise due to complexities induced by the interaction of the crack with various deformation mechanisms such as dislocation, micro twin, stacking faults etc.. As a first step toward the development of physics-based models of deformation in the presence of a crack, this paper proposes a comprehensive approach based on molecular dynamics simulations of a crystalline material with an embedded crack. The MD-based framework invokes a sequence of four tasks to accomplish the overall goal, viz. (i) MD simulation, (ii) characterization of atomic-level crack and deformation mechanisms, (iii) quantification of atomic-level deformation mechanisms and crack, and (iv) response analysis. Effective characterization methods like CNA, DXA and deformation gradient analysis followed by quantification are able to delineate the crack length/opening, dislocation structure and microtwins at a high resolution. Interactions of the crack with the dislocation networks and microtwins under mode I loading conditions are investigated for different lattice orientations. Crystal orientation has significant effect on the mechanisms activation and evolution. An important study is made through partitioning of the total energy into recoverable elastic energy, defect energy and inelastic dissipation, and correlating them with deformation characteristics such as dislocation density and twin volume fraction. Finally, a simple mechanistic model of deformation is developed, which associates dislocation density evolution with the stress–strain response in a crystalline material in the presence of a crack. Results show good quantitative agreement of material softening and hardening behavior with direct MD simulation results. The model can be further used to estimate the range of strain-rates that may be applied for physically meaningful MD simulations.

The concept of stored plastic work or frozen elastic energy in soil mechanics

This paper is part of a series that aims to explore systematically the applications of the modern theory of thermomechanics to the constitutive modelling of soils and other geomaterials. Although the division of the applied work into recoverable elastic energy and irrecoverable plastic energy is straightforward at the level of single grains, this is not true at the continuum level. Because of the highly heterogeneous nature of the stress and deformation fields at the micro level, some of the micro-level elastic energy is ‘frozen’, and consequently some of the applied plastic work is stored and is recoverable. The concept is explained at the micro level, at the meso level of the force chains, and at the continuum level. It is also explained in terms of a schematic spring–slider model. These ideas have very important ramifications for constitutive modelling at the continuum level. In particular it is shown that there are two causes for dilation in a soil, one due to Reynolds’ dilatancy, the other due to the recovery of the frozen energy (or stored plastic work). This has significant consequences for the concept of critical states. Implications for future research are indicated.

The concept of stored plastic work or frozen elastic energy in soil mechanics

This paper is part of a series that aims to explore systematically the applications of the modern theory of thermomechanics to the constitutive modelling of soils and other geomaterials. Although the division of the applied work into recoverable elastic energy and irrecoverable plastic energy is straightforward at the level of single grains, this is not true at the continuum level. Because of the highly heterogeneous nature of the stress and deformation fields at the micro level, some of the micro-level elastic energy is ‘frozen’, and consequently some of the applied plastic work is stored and is recoverable. The concept is explained at the micro level, at the meso level of the force chains, and at the continuum level. It is also explained in terms of a schematic spring–slider model. These ideas have very important ramifications for constitutive modelling at the continuum level. In particular it is shown that there are two causes for dilation in a soil, one due to Reynolds’ dilatancy, the other due to the recovery of the frozen energy (or stored plastic work). This has significant consequences for the concept of critical states. Implications for future research are indicated.

Scale effects in engineering failures

A brief review is given of what may be meant by a “catastrophic engineering failure”, particularly as it relates to situations involving fracture. Whether “fast fracture” is necessarily the same as “unstable” fracture—and whether it makes any difference anyway—is discussed. Since recoverable elastic energy, and irreversible remote plasticity, are volume-dependent quantities, but fracture work depends only on area, cube/square energy scaling principles are inherent in all mechanics of fracture. These different dependencies translate into the well-known experience that components and structures, made of materials which are appreciably ductile in laboratory-size testpieces, behave in a progressively less ductile fashion the larger they get. Eventually, above some critical size, their behaviour is globally elastic, and fractures are brittle. Conversely, when deformation zones are kept very small in normally-brittle materials, plastic deformation is possible, as shown by limiting sizes in the communication of powders and by the ability to micro-machine glass. Analytical studies and experimental investigations of scaled cracked bodies, covering the whole range from globally elastic in the large, through to quasi-rigid plastic in the small are described and assessed, including consideration of dynamic progressive fracture in frameworks.

Compression creep of molten poly(ethylene oxide)

Viscoelastic parameters of poly(ethylene oxide) in compression creep have been measured. Volume deformations ( k%) increase as pressure ( P) and temperature ( T) increase. Bulk creep compliance B( t) behaviour is different below and above certain critical values ( T c ≈ 393 K, and P c ≈ 30 MPa) assumed to correspond to the transition from helicoidal to planar conformations. Plots of B( t) versus time ( t) may be shifted to provide master curves, the pressure shift factors ( b p, a p) and the temperature shift factors ( b T, a T) increasing non-linearly as the pressure and temperature increase. The steady-state creep compliance ( B s) allows determination of the recoverable elastic energy ( B e). Volume viscosity ( η k) above 30 MPa remains almost constant, but decreases with increasing temperature.

Compression creep of molten polystyrene

AbstractViscoelastic parameters of polystyrene (PS) melt in compression creep have been measured in an lnstron capillary‐rheometer.Bulk compression creep compliance B(t) shows plateau regions in the molten state (B1) and the glassy state (Bg), both decreasing with increasing stress. Shifting of B(t) curves provides master curves suitable to analysing the total (superposed elastic and viscous deformations) bulk compression behaviour. The steady‐state creep compliance (Bs) allows to describe the recoverable elastic energy (Be) and seems to be related to the extrusion die swell (B/B). Volume viscosity (ηk) decreases with decreasing stress (P), increasing compression rates (k) and decreasing temperature (T).

Soil mechanics and plasticity analysis of strain softening

Plasticity concepts are set forth in a rather general manner for the treatment of soil as an isotropic strain-hardening or strain-softening material, and different assumptions are discussed for the derviation of incrementa stress-strain relations. Strain-softening flow laws violate Drucker's postulate, but it is shown how uniquencess can still be ensured by contraining the relative magnitude of the rate of strin softening with respect to the recoverable elastic energy of the material. The stability of the solutin is discuseed, and in order to illustrate the stability concepts, closed form solutions for the undrained expansion of a cylindrical cavity in a finite and infinite saturated medium are presented. Les concepts plastiques sont exposés de façon générale en vue du traitement du sol comme un matériau isotrope présentant des comportements de raffermissement aussi bien que de ramolissement. Différentes hypothèses por la dérivation des lois incrémentales contraintes-déformations élementaires sont discutées. Les lois de comportement de ramollissement ne satisfont pas le postulat de Drucker, cependant il est montré comment l'unicite peut être assurée en fixant la grandeur relative du taux de ramollissement par rapport à l'énergie élastique récuperable du matériau. La stabilité de la solution est discutée. De façon à illustrer les concepts de stabilité, sont présentées des solutions littérales pour l'expansion non drainée d'une cavité cylindrique dans un milieu saturé fini et infini.

Influence of the die entry angle on the entrance pressure drop, recoverable elastic energy, and onset of flow instability in polymer melt flow

AbstractAn experimental study has been carried out to investigate the effects of die entry angle on the entrance pressure drop, recoverable elastic energy, and onset of melt fracture in the flow of viscoelastic polymeric melts through a capillary die. For the study, capillaries with an L/D ratio of 4 and with varying die entry angles, 15°, 30°, 60°, 90°, 120°, and 180°, were used for extruding low‐density polyethylene and high‐density polyethylene. Measurements were taken of wall normal stresses along the upstream reservoir section, tapered conical section, and straight capillary section.

Influence of reservoir diameter on the melt elasticity in capillary flow

AbstractAn experimental study has been carried out to investigate the influence of the reservoir‐to‐capillary diameter (DR/D) ratio on the elastic properties of polymer melts flowing through capillary tubes. For the study, a capillary rheometer, described in an earlier paper by Han, was used with DR/D ratios of 3, 6, 9 and 12. Measurements were taken of wall normal stresses in high density polyethylene along the axis of the capillary, and the axial pressure profile was used to obtain the “exist pressure,” which is believed to be an elastic phenomenon. The analysis of the experimental data indicates that, for a given capillary length‐to‐diameter (L/D) ratio, the exit pressures first increase and then level off, as the DR/D ratio is increased. This behavior of the exit pressure is in accord with that of extrudate expansion which has also been determined in the experiment. This dependence of the exist pressure and extrudate expansion ratio on DR/D ratio is explained with the concept that the amount of recoverable elastic energy stored in the melt flowing through the capillary depends on the strain history, which the melt experiences on entering the capillary.