Modelling non-linear stress–strain behaviour of rubber toughened plastics

Abstract

An elastic–plastic model has been developed for describing the non-linear, stress–strain curves of rubber toughened plastics. Following a linear elastic response at low strains, it is assumed that the material undergoes plastic deformation which, for dilatational stress states, is enhanced by the generation and growth of cavities within the rubber particles. The model is based on Gurson's theory of plasticity in porous materials and follows the developments proposed by Bucknall and co-workers. Parameters are included that allow for the effect of pressure on the yield stress of the matrix material between the cavities and for the influence of void interactions on matrix shear banding. Account is also taken of the change in matrix composition, and hence the matrix yield stress, during void nucleation. The nucleation is assumed to occur over a critical range of volumetric strain ε_V and to involve the replacement of rubber particles by an equal volume of effective cavities. Two different nucleation functions have been investigated to describe the dependence of the effective void fraction on ε_V.

Equations that govern the elastic, yield and flow behaviour under multiaxial stress states have been solved to determine required material parameters and to predict behaviour in tension and compression from shear hardening data. The predicted and observed behaviour show good agreement, indicating that the model may be applied with some confidence to stress analyses using finite element calculations.     

The effects of surface texture on natural rubber/metal friction at high pressures

Abstract

A technique is described that allows the friction of rubber on metal at high pressures (up to 15 MPa) to be measured. A series of experiments were performed investigating the behaviour of rubber under these conditions and the effects that the track surface texture had. It was found that Thirion's law remained effective for describing the friction of rubber under these conditions. It was also observed that, at ~5 MPa, a crossover occurred and at higher pressures, the smooth tracks resulted in lower friction.     

Optimizing maximum equivalent strain on solder balls in flip‐chip packages

Flip‐chip packaging provides a high‐performance low‐cost approach for development of electronic packages. A three‐dimensional (3D) viscoelastic‐plastic finite element analysis using the commercial software ANSYS has been performed to study the thermo‐mechanical behavior in flip‐chips assemblies, i.e., the four components: chip, solder ball, underfill, and substrate. The viscoelastic behavior of underfill is modeled by a Maxwell constitutive equation, while the viscoplastic behavior of solder balls is modeled by an Anand model. Both chip and substrate are assumed to elastic materials modeled by Hooke's law. As in standard industry practice, temperature cycling from 125 to −40°C is used. Thermo‐mechanical behavior of solder balls is presented, and the effects of underfill material properties are investigated. Further, Taguchi methods are used to optimize flip‐chip package performance. The design goal is to minimize the maximum equivalent strain on the solder balls. The eight flip‐chip assembly factors chip‐thickness/substrate‐thickness ratio, underfill modulus (G_i), underfill relaxation time (λ_i), solder height‐to‐diameter ratio, chip coefficient of thermal expansion (CTE), underfill CTE, solder CTE, and substrate CTE are chosen for optimization. POLYM. COMPOS., 2008. © 2007 Society of Plastics Engineers     

Dynamic behaviour and visco-elastic damage model of ultra-high performance cementitious composite

The dynamic behaviour of ultra-high performance cementitious composite (UHPCC) with compressive strength of 200 MPa with different steel fiber volume fractions was studied under impact using the split Hopkinson pressure bar. Three aspects of the testing: a gimbal device, wave shaping and direct strain measurement, were used to increase experimental accuracy. Results indicate that UHPCC has obvious strain rate effects. The peak stress, peak strain, elastic modulus and the area under the stress–strain curve increase with increasing strain rate. When the strain rate exceeds a threshold value, specimens with and without fibers begin to fracture. At high strain rate the unreinforced specimens fracture into small parts while fiber reinforced ones only have fine cracks on the edges. A visco-elastic damage model of UHPCC is proposed based on a nonlinear visco-elastic model (the ZWT model) and the material damage measured by the ultrasonic wave velocity method.     

Characterisation of cut and chip behaviour for NR,SBR and BR compounds with an instrumented laboratory device

ABSTRACT

Understanding the cut and chip (CC) effect in rubber is important for successful product development for tires used in off-road or poor road conditions and for other demanding applications of rubber. This research describes a laboratory testing method for characterising the CC fracture behaviour of rubber using a device that controls and records multiple applied loads and displacements during cyclic impact to the surface of a solid rubber specimen to mimic and quantify the CC damage experienced by tire tread compounds. To study the capabilities of the instrument, three model compounds were studied that are based on carbon black reinforced compounds of common elastomers used in tire treads: natural rubber (NR), styrene-butadiene rubber (SBR), and butadiene rubber (BR). These polymers have well-established CC tendencies in field performance of tire treads, with NR exhibiting the best CC resistance followed by SBR and finally BR. The same trend was found with the rubber impact testing approach that allowed the CC behaviour to be quantified using a new physical parameter which is the CC propensity (P). The relative ranking for CC resistance for the three compounds followed the fatigue crack growth resistances of the materials but was exactly opposite to the ranking of DIN abrasion resistance. This provides evidence that CC damage from impact by mm-scale asperities and abrasion of rubber against μm-scale asperities exhibit distinct characteristics in rubber.     

Experimental and computational aspects of cavitation in natural rubber

Abstract

General constitutive equations for hyperelastic materials are based on the first law of thermodynamics whereby the total strain energy function is expressed either in terms of strain invariants or principal stretches. For most applications the strain energy functional does not need to include dilatational components. However, the pressure–volume relationship for nearly incompressible materials must be explicitly accounted for when rubber components are highly constrained. Thus, the hyperplastic response needs to be expressed in terms of dilatational and deviatoric components. Experimental evidence has been reviewed to show that rubber is subjected to a loss of stiffness attributed to cavitation damage when subjected to a hydrostatic tensile stress state. The critical pressure is identified for which microscopic material imperfections will tear open to form internal bubbles and cracks.

Cavitation damage in rubber is associated with a significant reduction in the bulk modulus. Thus, a variable bulk modulus can best be used to describe the behaviour of rubber when cavitation damage occurs. The introduction of a cavitation damage modulus is suggested as a simple approach to represent realistically the mechanics of cavitation in rubber solids.     

Mathematical model of ball wear in grinding mills II. General solution

Transient solutions to the population balance model of ball wear are given for various wear kinetics. At steady state, a single equation suffices to describe the ball size distribution and the ball consumption for any wear rate. The effect of wear rate law, design factors and operating conditions on the size distribution of balls and steel consumption were studied via simulation techniques and a method is given to combine data from marked ball tests and screening of the mill charge in order to determine unambiguously wear kinetics in industrial mills.     

A Knowledge Base of the Functional Properties of the Conveyor Belt Adhesive Joint for FEM Simulation of Its Stress and Strain State

Abstract

This paper describes a step-by-step procedure for creating a knowledge base of the functional properties of multi-ply rubber conveyor belts. The knowledge was gathered during laboratory studies of the operational features of belts and their joints which had been manufactured using various bonding methods. The measurements were done on the conveyor belts at different stages of their use and also under industrial conditions. The results of the laboratory studies were used to verify a numerical model developed for a typical conveyor belt adhesive joint manufactured from several rubber materials with different properties. The development of the finite element numerical model was preceded by strength tests aimed at identifying the strength properties of the rubber materials used as the constituent elements of the joint. The causes of previous errors made in the course of preparing material models for numerical simulation were described and a proper method for carrying out strength tests was proposed. The collected data and the numerical model of the joint were used to perform a simulation of the state of stress and strain in the area of the joint. This made possible a detailed analysis of the processes occurring within the joint in terms of fatigue performance. The numerical model can be used in the analysis and optimization of various joint structures made from rubber materials with different strength properties. An analysis was also carried out of the influence of the thickness of the adhesive layer on the strength of a joint to illustrate the possibility of using the developed model for the optimization of joint geometry. The goal of the numerical analysis was to estimate the possibility of using the developed model of the joint for predicting the durability and strength of the joint, as well as using it at the structural design stage of the joint.     

Polystyrene composites containing crosslinked polystyrene‐multiwalled carbon nanotube balls

Crosslinked polystyrene‐multiwalled carbon nanotube (PS‐MWCNT) balls, which act as conductive microfillers, were prepared by the in situ suspension polymerization of styrene with MWCNTs and divinyl benzene (DVB) as a crosslinking agent. The diameters of the synthesized crosslinked PS‐MWCNT balls ranged from 10 to 100 μm and their electrical conductivity was about 7.7 × 10^?3 S/cm. The morphology of the crosslinked PS‐MWCNT balls was observed by scanning electron microscopy and transmission electron microscopy. The change in the chemical structure of the MWCNTs was confirmed by Raman spectroscopy and Fourier transform infrared spectroscopy. The mechanical and electrical properties of the PS/crosslinked PS‐MWCNT ball composites were investigated. It was found that the tensile strength, ultimate strain, Young's modulus, and impact strength of the PS matrix were enhanced by the incorporation of the crosslinked PS‐MWCNT balls. In addition, the mechanical properties of the PS/crosslinked PS‐MWCNT ball composites were better than those of the PS/pristine MWCNT composites. © 2008 Wiley Periodicals, Inc. J Appl Polym Sci, 2008     

Characterisation of vulcanised natural rubber behaviour by monotonic and in situ cyclic X-ray scattering tests

Abstract

The effect of curing and loading conditions on the mechanical response of natural rubber are investigated by monotonic and in situ X-ray cyclic tensile tests. Tests are conducted on four samples, which differ by vulcanisation conditions. Samples are subject to two strain rates (2.7?×?10^??3 s^??1 and 16.66?×?10^??3 s^??1), and numerous imposed elongation levels range from 450 to 900%. The coupling between the strain rates and the elongation levels on the stress softening evolution resulting from strain induced crystallisation is investigated. In situ thermomechanical tensile cyclic test is performed in order to withdraw the effect of the strain induced crystallisation on the maximum stress decrease. The experimental results analysis shows that an optimum vulcanisation condition (150°C, 30?min) enhances the hardening process in the monotonic loading due to the strain induced crystallisation. However, under optimum curing conditions, cyclic loading induces a large hysteresis loss, a high stress softening and a high degree of strain induced crystallinity. The material softening sensitivity is controlled by coupled effect of strain ranges and elongation levels. This panoply of experimental measurements present a key information for material parameters identification that are useful to predict the lifetime of engineering components made of natural rubber such as racks, laminated rubber bearings and tires.     

固-液两相管式膜清洗系统的研究

本文主要研究了用海绵橡胶球(固)一水(液)两相清洗系统对淀粉溶液污染的管式膜的清洗效果。通过海绵橡胶球清洗与传统大量水冲洗方法对水通量恢复率和蛋清截留率的比较,得出了海绵橡胶球清洗方法具有良好的清洗效果,并且对膜孔径无明显影响的结论。     

A constitutive model for the nonlinear viscoplastic behavior of thermoplastic olefin

A tangent constitutive model was developed in this article to address the nonlinear viscoplastic behavior of compound grade thermoplastic olefin (TPO). The TPO was commonly blends of polypropylene matrix, rubber, and inorganic filler. The constitutive model for TPO was obtained from the combination of the mechanical behavior of the matrix and fillers. In a multiphase material, the rate‐dependent behavior of polypropylene matrix was presented by a physically based constitutive model for large strain deformation, while the deformation behavior of rubber and talc were captured by Hooke's law. The average strain of each phase, as well as the strain of the voids caused by cavitation of rubber and debonding of talc, was determined by the Mori‐Tanaka method, in conjunction with a tangent modulus approach. To test the applicability of the developed model, it was applied to calculate the rate dependent stress‐strain relations of TPO. The model was predictive of the initial rate‐dependent stiffness, yield, and strain hardening response in large strain deformation. The constitutive model was incorporated into a finite element code to predict the large strain deformation behavior of TPO. The initiation of necking and neck propagation were obtained and confirmed by experimental observation. POLYM COMPOS., 2010. © 2009 Society of Plastics Engineers     

原油对丁腈橡胶密封件性能的影响

以原油为试验介质,模拟井况研究原油对丁腈橡胶密封件性能的影响。结果表明,在模拟井况条件下,丁腈橡胶密封件出现老化现象,随着浸泡时间的延长,密封件的拉伸强度和扯断伸长率逐渐下降,硬度逐渐增大,老化机理以分子链交联老化反应为主;随着温度的升高,老化速率快速增大;高含水率的原油对丁腈橡胶密封件的性能存在负面影响。     

Effect of fiber properties and matrix composition on the tensile behavior of strain-hardening cement-based composites (SHCCs) subject to impact loading

The article at hand describes the behavior of high-strength and normal-strength strain-hardening cement-based composites (SHCCs) made of fine-grained matrix and high-density polyethylene fibers under quasi-static and impact tensile loading. The dynamic tension testing of unnotched and notched cylinders was performed using the Hopkinson bar at strain rates of around 150 s^− 1. The responses of the materials under dynamic and quasi-static tensile loading were compared to the corresponding results for normal-strength SHCC made of polyvinyl-alcohol fibers as obtained in previous investigations. To explain the pronounced differences in rate effects on the material performance of various SHCC compositions, cracking pattern and fracture surface conditions were studied. Additionally, strain rate dependent changes in the mechanical behavior of individual fibers and in the fiber–matrix interfacial properties were deduced from single-fiber tension tests and fiber pullout tests, respectively. Altogether, the results obtained provide clear indications as to the decisive parameters for a purposeful material design of impact resistant types of SHCC for use in structural elements or protective overlays.     

Scientific Principles of Drying Technique (in Russian)B.S. Sazhin and V.B. Sazhin Nauka,Moscow, 1997, 448 pages

ABSTRACT

A novel low cost tray dryer equipped with a solar air collector, a heat storage cabinet and a solar chimney is designed and tested. The design is based on energy balances and on an hourly-averaged radiation data reduction procedure for tilted surfaces. Measurements of total solar radiation on an horizontal plane, ambient temperature and humidity, air speed, temperature and relative humidity inside the dryer as well as solids moisture loss-in-weight data are employed as a means to study the performance of the dryer. First, detailed diagnostic experiments are carried out with no drying material on the trays. Next, a number of experiments is conducted using a controlled reference material whose reproducible dehydration pattern allows comparisons among runs. Drying is also tested during night operation and under adverse weather conditions. For all the employed conditions, the material gets completely dehydrated at a satisfactory rate and with an encouraging system's efficiency.     

Swelling behaviour of rubber vulcanizates: 2. Effects of tensile strain on swelling

The effects of tensile strain on the swelling behaviour of acrylonitrile-butadiene copolymer rubber vulcanizates were studied by real-time pulsed nuclear magnetic resonance (n.m.r.) measurements and volume swelling measurements at equilibrium. It was shown that tensile strain causes an increase of the initial swelling rate evaluated by n.m.r. measurements and of the swelling ratio of the rubber matrix at equilibrium. This behaviour was discussed qualitatively in terms of the molecular mobility of the network chains on the basis of Treloar's theory for swelling under deformation. It was suggested that the presence of reinforcing fillers in the rubber matrix exerts two noticeable effects on swelling under deformation: (1) a transient effect through some oriented structure induced by stretching, which restricts the increase of the swelling rate; (2) a strain amplification effect, which causes the increase of the average local strain in the rubber matrix and enhances the swelling ratio more remarkably proportional to the filler concentration as compared with that of the unfilled system.     

Detection of cavitation in rubber phase of rubber toughened poly (methyl methacrylate) using thermal contraction measurements

Abstract

Measurements of mechanical properties and thermal expansion–contraction behaviour have been carried out on plain PMMA and on a transparent grade of rubber toughened (RT) PMMA. Uniaxial tensile tests at 23°C show that the stress–strain (σ–ε) curve for the RTPMMA begins to deviate from linearity at ε ≈ 1·5%, and reaches a load maximum at ε ≈ 6·7%. Visible whitening begins at ε ≈ 1·5%, and intensifies with increasing strain, but annealing for 3 h at 115°C restores the material to its initial transparent condition. Thermal expansion and contraction tests show that pre-straining to ε ≥ 2% produces a marked decrease in the coefficient of thermal expansion (CTE) of RTPMMA over the temperature range -20 to +50°C, where the rubber is above its T _g. Lower pre-strains have little effect on expansion–contraction behaviour. Annealing after pre-straining leaves the CTE unchanged at its reduced value if the pre-strain is above 3%. However, it causes an increase in CTE towards its initial value in specimens pre-strained to ε= 2%. This work provides clear evidence for cavitation in the rubber particles. It also shows that annealing after pre-straining does not completely restore the rubber's resistance to cavitation. Creep tests at 23°C on pre-strained specimens, both before and after annealing, demonstrate that rubber particle cavitation promotes a substantial acceleration in strain rates.     

The Charpy impact fracture behaviour in ABS materials

The effects of rubber content and temperature on impact fracture behaviour of ABS materials with rubber particle diameter of 110 nm were studied by means of an instrumented Charpy impact tester which can record a load-deflection curve at impact fracture. From the load-deflection curves, some important parameters, such as the maximum impact load, the maximum deflection, the J-integral corresponding to the total impact absorbed energy, dynamic yield stress and Young's modulus etc. were obtained and their rubber content and temperature dependencies were investigated. Stable crack extension and plastic zone size are studied as a function of rubber content and temperature by the use of optical microscope. The fractured surfaces were observed using a scanning electron microscope to clarify the fracture mechanism under impact condition.     

Fatigue peeling at rubber interfaces

Abstract

A fatigue peeling test has been developed to evaluate the failure of rubber to rubber interfaces under cyclic loading. Results obtained through this method have been compared to those of a typical fatigue crack growth experiment. The results show that the trends between these two failure modes are similar with the peeling necessary to drive the crack being slightly higher than the strain energy release rate at the same crack growth rate. Cyclic and time dependent contributions to the fatigue crack growth behaviour have been calculated using this test for an styrene–butadiene rubber compound and the results appear to be consistent with previous work although the origin of the cyclic contribution remains uncertain. The influence of pressure at the interface during vulcanisation has also been investigated and it has been observed that the fatigue peel behaviour is proportional to the surface area of contact developed during the curing cycle.     

Models for the behavior of boron carbide in extreme dynamic environments

We describe models for the behavior of hot-pressed boron carbide that is subjected to extreme dynamic environments such as ballistic impact. We first identify the deformation and failure mechanisms that are observed in boron carbide under such conditions, and then review physics-based models for each of these mechanisms and the integration of these models into a single physics-based continuum model for the material. Atomistic modeling relates the composition and stoichiometry to the amorphization threshold, while mesoscale modeling relates the processing-induced defect distribution to the fracture threshold. The models demonstrate that the relative importance of amorphization and fracture are strongly dependent on the geometry and impact conditions, with the volume fraction of amorphized material being unlikely to be significant until very high velocities (~3 km/s) are reached for geometries such as ball impact on plates. These connections to the physics thus provide guidelines for the design of improved boron carbide materials for impact applications.