Development of viscoplastic strains during creep in continuous fibre GMT composites

This work is part of a larger study aimed at characterizing the viscoelastic–viscoplastic behavior of a continuous fiber glass mat thermoplastic composite. The purpose of this paper is to experimentally and numerically decouple the viscoplastic strains from total creep response. This enabled the characterization of the evolution of viscoplastic strains as a function of time, stress and loading cycles. The separation also allowed viscoplastic strain development to be corresponded with the progression of failure mechanisms such as interfacial debonding and matrix cracking which were captured in situ. This was achieved by performing creep tests at seven stress levels between 20 and 80 MPa. For each stress level, a series of creep-recovery tests were performed on single specimen for increasingly longer durations from 1 to 24 h. Stress and time dependence of viscoplastic strains were determined experimentally. Using part of the data generated, a viscoplastic model was developed following a method proposed by Nordin. The model had excellent agreement with experimental results for all stresses and times considered. In multiple loading cycles, the viscoplastic strain development is accelerated with increasing number of cycles at higher stress levels. The results further verify the technique for numerical separation of viscoplastic strains proposed in an earlier work. Finally, it was found that the development viscoelastic strains during creep are affected by the previous viscoplastic strain history.     

Explicit forms for the tangent modulus tensor in viscoplastic stress analysis

Viscoplastic constitutive models typically lead to compliance (strain–stress) relationships, which must be inverted for use in the finite element displacement method. Computational requirements can be increased significantly for models of practical size due to the large number of matrix inversions which are necessary. This paper describes a method of obtaining the required stress–strain relations analytically, thus eliminating the need for numerous matrix inversions in the solution. The technique is applicable to a number of commonly-used viscoplastic models, as demonstrated in the examples.     

Uniaxial nonlinear viscoelastic viscoplastic modeling of polypropylene

This paper presents the application of the Schapery viscoelastic and the Perzyna viscoplastic models to strain recovery data of polypropylene. In a previous study, the recovery of strain after monotonic uniaxial tensile loading was measured to gather information on the viscoelasticity and viscoplasticity. The viscoplastic strains from several load histories were determined and are used to calibrate the viscoplastic model. The parameters of the one-dimensional Schapery model are then found by nonlinear optimization using the strain recovery history. The prediction of stress relaxation and creep behavior is investigated.     

考虑塑性徐变的高混凝土坝实测应变转换应力探讨

将应变计组实测应变转换为应力与混凝土的应力状态有关。针对高混凝土坝应力作用水平较高,当混凝土的应力超过一定的限度,混凝土将进入塑性徐变阶段,如果仍基于弹性徐变体的应力-应变关系进行实测应变的应力转换,获得的应力与实际情况不符。该文假设混凝土在高应力作用下将产生塑性流动,根据P.Perzyna假设计算黏塑性应变率,首先推导了最大拉应力屈服准则和Hsieh-Ting-Chen屈服准则的黏塑性应变率计算公式,接着推导了考虑塑性徐变的实测应变转换应力的计算公式,进而探讨了考虑塑性徐变的高混凝土坝实测应变转换为应力。实例分析表明:由于将实测应变转换为应力采用增量法进行计算,在转换过程中,某阶段的应力失真,必然导致后续转换应力的真实性,而考虑塑性徐变的实测应变转换的应力更符合实际情况。     

Finite element implementation of a macromolecular viscoplastic polymer model

This paper presents a time‐integration method for a viscoplastic physics‐based polymer model at finite strains. The macromolecular character of the model resides in (i) the viscoplastic law based on a double‐kink molecular mechanism, and (ii) a full chain network model inspired by rubber elasticity to describe the large‐strain orientation hardening. A back stress enters the constitutive model formulation. Essential aspects of a three‐dimensional finite‐element implementation are outlined, the main novelty being in the back stress formulation. The computational efficiency and accuracy of the algorithm are examined in a series of parameter studies. In addition, because a co‐rotational formulation of the constitutive equations is employed using the Jaumann rate in the hypoelastic equation and the back stress evolution equation a detailed analysis of stress oscillations is carried out up to very large strains in simple shear. Subsequently, three‐dimensional FE analyses of compression with friction and instability propagation in tension are used as a means to demonstrate the robustness of the implementation and the potential occurrence of stress oscillations and shear bands in large‐strain analyses. Copyright © 2013 John Wiley & Sons, Ltd.     

一种考虑尺寸效应的颗粒材料流变模型及其验证

经典连续介质理论的粘塑性本构关系缺乏材料尺度的相关性,难以表征颗粒材料流变的尺寸效应,而Cosserat连续体中的内禀特征长度为刻画材料的尺寸效应提供了一种可能途径。该文旨在Cosserat连续体的理论框架下发展Perzyna粘塑性模型,以探讨颗粒材料流变的尺寸效应与影响机制。首先基于Drucker-Prager屈服准则导出了Cosserat连续体粘塑性模型的一致性算法,获得了过应力本构方程积分算法与一致切向模量的封闭形式,并在ABAQUS二次平台上采用用户自定义单元(UEL)予以程序实现。有限元数值算例模拟了软岩试样的三轴压缩蠕变和两种堆石料试样在常规三轴条件下的蠕变和应力松弛,数值预测结果与相应试验结果具有较好的一致性,表明该流变模型的适应性。同时,将颗粒的球型指数、圆度和平均粒径作为表征颗粒材料内禀特征长度的一种度量,以反映颗粒材料的试样尺寸及其颗粒粒径与形状对流变过程中的轴向应变、偏应变和偏应力的影响关系,表明所发展的流变模型可以捕捉颗粒材料流变行为的压力相关性和尺寸效应。     

A continuous threshold model for the visco-elasto-plastic behavior of PET based multi-layer polymeric films

The envelopes of the super-pressure balloons fabricated by the French space agency (CNES) are made of a multi-layer polymeric film that shows substantial viscoelastic and viscoplastic behavior, both depending nonlinearly on stress. A model is presented that takes into account stress depending viscoelastic and viscoplastic strain response functions observed in uniaxial creep experiments. For easy numerical implementation, the strain response functions are represented by a Prony series, whose coefficients form a continuous spectrum on the logarithmic retardation time scale. The observed response functions are generated by an exponential power law distribution of the Prony coefficients with exponent 3. The distribution is fully characterized by three stress dependent parameters: its center, width, and an intensity factor, corresponding to the maximum coefficient. Creep and recovery experiments show that both viscoelastic and viscoplastic strain are highly stress dependent over a limited stress range and are approximately linear at low stresses and around the maximum stress reached during flight. A continuous threshold function is proposed that approximates well the observed stress dependence of the intensities. It is assumed that the other viscoelastic (viscoplastic) parameters change around the same threshold as the viscoelastic (viscoplastic) intensity and are approximately constant elsewhere. The model reproduces very well the strain response observed in creep and recovery experiments with different creep stresses.     

Thermodynamically consistent coupled viscoplastic damage model for perforation and penetration in metal matrix composite materials

Accurate modeling and efficient analysis of the metal matrix composite materials failure mechanism during high velocity impact conditions is still the ultimate goal for many researchers. The objective is to develop a micromechanical constitutive model that can effectively simulate the high impact damage problem of the metal matrix composite materials. Therefore in this paper, a multiscale micromechanical constitutive model that couples the anisotropic damage mechanism with the viscoplastic deformation is presented here as a solution to this situation. This coupled viscoplastic damage model is formulated based on thermodynamic laws. Nonlinear continuum mechanics is used for this heterogeneous media that assesses a strong coupling between viscoplasticity and anisotropic damage. It includes the strong directional effect of the fiber on the evolution of the back stress and the development of the viscoplastic strain in the material behavior for high velocity impact damage related problems.     

On the influence of preloading in the nonlinear viscoelastic–viscoplastic response of carbon–epoxy composites

On an ongoing research for the nonlinear viscoelastic response of composites and polymers, a study of the influence of preloading applied to composite laminates subjected to creep–recovery loading is performed. In cases where high stress levels are applied, this response becomes highly nonlinear and has to be taken into account when designing composite parts. A major problem encountered in the experimental investigation of the nonlinear viscoelastic behaviour is the mode of the initial applied loading and its effect in the overall viscoelastic response of the test sample. The damage that occurs due to the instantaneous application of the load leads to an additional viscoelastic/viscoplastic strain component. In order to investigate this effect as well as to compare different preloading modes, as far as viscoelastic/viscoplastic response is concerned, a test program was initiated and the experimental data were investigated in the current study. A preloading mode is applied in each specimen prior to the creep–recovery testing at different applied stress levels. Useful results concerning the effect of preloading in the time dependent response of the material are concluded. Variation of the values of viscoplastic strain in respect to the preloading mode is also of great concern.     

Sharp V‐notches in viscoplastic solids: Strain energy rate density rule and fracture toughness

Different from Neuber's rule or Glinka's energy method which are always adopted to characterize the notch tip field under elastoplastic condition, in this paper, the strain energy rate density (SERD) rule is used for viscoplastic materials. In particular, based on the definition of generalized notch stress intensity factor (G‐NSIF) for sharp V‐notch in viscoplastic solids, the concept of SERD for sharp V‐notch in viscoplastic solids is presented. Subsequently, by taking as a starting point the SERD, the averaged strain energy density (SED) for sharp V‐notch in viscoplastic solids is derived with integration of time. The fracture toughness relation between sharp V‐notch specimens and crack specimen in viscoplastic materials is given based on the transformation of SERD. A numerical approach is presented to compute the SERD and SED based on finite element method. Some crucial comments on the G‐NSIF have been discussed. Some typical solutions for SERD and SED for sharp V‐notched specimens are investigated.     

Plastic deformation in electrical conductors subjected to short-duration current pulses

In this paper, we consider the viscoplastic response of Al 6061-T6 and Cu-102 when subjected to a combination of mechanical load and high-intensity electric current. The specimens are subjected to mechanical loading under fixed-grip and dead-load conditions; in addition, the specimen is subjected to a nearly sinusoidal current pulse (frequency 4 kHz, duration ∼1 ms, and intensity ∼10⁹ A/m²). The resulting temperature increase causes the yield stress to drop and enables accumulation of plastic strain. A viscoplastic model is used to simulate the process; comparisons of the simulation results to time resolved measurements of strain and temperature are used to calibrate the viscoplastic model.     

Prediction of welding buckling distortion in a thin wall aluminum T joint

In this paper, local and global welding buckling distortion of a thin wall aluminum T joint is investigated. A thermo-elastic–viscoplastic model is employed to determine longitudinal residual stresses; analysis of thermal model and elastic–viscoplastic (Anand) model are uncoupled. Molten puddle motion (speed of welding) is modeled by using time dependent birth and death element method. Three dimensional nonlinear-transient heat flow analysis has been used to obtain the temperature distribution, and then by applying thermal results and using three dimensional Anand elastic–viscoplastic model, stress and deformation distributions are obtained during welding and after cooling. Local buckling is investigated by analyzing the history of stress and strain relations. Local buckling is assumed to occur at a point if a small change in the magnitude of stress causes large deformation during of the welding process. By applying residual stresses on a structural model and using eigenvalue methods, global buckling instability of the welded structure is determined.     

Viscoplasticity of Steamed Wood

Plasticity of steamed Spruce wood, compressed in uniaxial strain, is addressed in terms of a classical linear viscoplasticity model. The dynamic stiffness modulus increases along with compressive stress in the radial material direction, but decreases as a function of stress in the longitudinal direction. The longitudinal viscoplastic retardation time is an order of magnitude smaller than the radial retardation time, the plastic strain rate at invariant normalized overstress thus being much higher in the longitudinal direction. In the longitudinal direction, the retardation time increases along with increased compressive stress. The viscoplastic retardation time is inversely proportional to the straining rate in both material directions. Consequently, within any particular schedule of normalized overstress, the accumulation of plastic strain along with the number of loading cycles is independent of straining rate.     

Viscoplastic analysis of structural polymer composites using stress relaxation and creep data

A structural carbon based composite material has been investigated for its high temperature viscoplastic properties using a model based on an overbearing stress concept and using the data obtained from load relaxation and creep. The time dependent viscoplastic properties were obtained at several load and temperature levels. An elastic–viscoplastic constitutive model (proposed by Gates) was used for the modeling efforts. The model is based on an overstress concept appropriate to inelastic properties of composites. The materials parameters for the model are obtained from a set of load relaxation experiments. The model predictions have been compared to the results of creep tests. The results show that the model is capable of predicting the creep behavior at shorter time periods and lower temperatures. As the temperature is increased or as the creep is prolonged the model predictions deviate from the experimental results.     

Creep failure time prediction of polymers and polymer composites

A theoretical approach for the prediction of creep rupture time of polymers and polymer composites is analyzed in the present work. This analysis takes into account the viscoelastic path at small strains and the viscoplastic path at higher stresses. The calculation of the rate of creep strain is based on a thermally activated rate process, while the emergence and growth of plastic strain, with increasing creep time, is also taken into account. When the accumulated strain attains values, high enough to lead to failure, its slope versus time exhibits an abrupt change. At this specific time, the creep rate function in respect to time appears a minimum. The creep failure time is defined as the time where the creep rate takes its minimum value. The model has been tested for various types of polymeric materials, as well as for polymer composites. Once the model parameters are estimated from short time creep strain data, then it was proved to successfully predict the creep failure time at a variety of stress levels, for all material types examined.     

Effect of an interphase region on debonding of a CNT reinforced polymer composite

The effect on stiffness and debonding of an interphase zone of altered polymer properties surrounding each carbon nanotube (CNT) in a CNT reinforced polymer composite is investigated. The interphase zone has position dependent material properties that merge with those of the polymer at a sufficiently large distance from the inclusion. There is evidence that such an interphase zone must be included in models in order to represent the overall composite properties. The analyses are based on an axisymmetric unit cell model of the composite. An elastic–viscoplastic conventional continuum constitutive relation (a size-independent relation between stress, strain and strain rate) is taken to characterize the bulk polymer material and the interphase, with the material properties being position dependent in the interphase. The interface between the polymer and the CNT is modeled by a phenomenological cohesive relation that allows for complete separation and the creation of new free surface. The effect of varying interface strength on the composite stress–strain response and on debonding is analyzed both with and without an interphase. The presence of an interphase increases the composite stiffness but promotes debonding which ultimately reduces composite stress carrying capacity. The compliance of the interface also affects the stress–strain response prior to debonding and leads to stress redistributions within both the fiber and the matrix (and/or interphase) which can affect the fracture mode that occurs.     

A semi-analytical integration method for the numerical simulation of nonlinear visco-elasto-plastic materials

A semi-analytic integration method is proposed, which can be used in numerical simulation of the mechanical behavior of nonlinear viscoelastic and viscoplastic materials with arbitrary stress nonlinearity. The method is based upon the formalism of Prony series expansion of the creep response function and accepts arbitrary stress protocols as input data. An iterative inversion technique is presented, which allows for application of the method in routines that provide strain and require stress as output. The advantage with respect to standard numerical integration methods such as the Runge-Kutta method is that it remains numerically stable even for integration over very long time steps during which strain may change considerably due to creep or recovery effects. The method is particularly suited for materials, whose viscoelastic and viscoplastic processes cover a very wide range of retardation times. In the case of simulation protocols with phases of slowly varying stress, computation time is significantly reduced compared to the standard integration methods of commercial finite element codes. An example is given that shows how the method can be used in three dimensional (3D) constitutive equations. Implemented into a Finite Element (FE) code, the method significantly improves convergence of the implicit time integration, allowing longer time increments and reducing drastically computing time. This is shown in the case of a single element exposed to a creep and recovery cycle. Some simulations of non-homogeneous boundary value problems are shown in order to illustrate the applicability of the method in 3D FE modeling.     

Creep failure of polypropylene: experiments and constitutive modeling

Observations are reported on isotactic polypropylene in uniaxial tensile tests with various strain rates, relaxation tests with various strains, and creep tests with various stresses at ambient temperature. Constitutive equations are derived for the viscoelastic–viscoplastic responses and damage of a semicrystalline polymer at three-dimensional deformations. Adjustable parameters in the stress–strain relations are found by fitting the experimental data. The model is applied to predict creep-failure diagrams in the entire interval of stresses. A phenomenological approach is proposed to determine a knee stress, at which transition occurs from ductile to brittle rupture. Accuracy of this method is evaluated by numerical simulation.