Strain rate effects in fracture of polymer modified cements

Abstract

Because of the role of the polymer in governing the fracture behaviour of polymer modified (ICI ‘NIMS’) cements, it is of considerable importance to investigate the effects of strain rate. Creep rates in polymers are generally higher than those associated with cement or concrete; this is particularly the case when a polymer is plasticised. One of the most effective plasticisers for a water soluble polymer is obviously water. It is known that polymer modified cements suffer a relatively rapid loss of strength on immersion in water. However, this loss will be exacerbated by creep effects, especially in the presence of stress concentrations, resulting in fracture through stress corrosion processes. This paper presents recent data obtained on these problems for both Portland and calcium aluminate cements.

MST/717     

Strain induced fracture in low strength steels

This paper attempts to investigate the role of strain in the fracture of low strength steel in the temperature range of −196 to 28°C and at the crack tip strain rate range of 10⁻⁵ to 10°/sec. The tensile test data is suitably processed to estimate the fracture strain in the fracture toughness specimen. The micro-fractographic observations help to identify the microfracture mechanisms and relate them with the governing fracture criteria. Even for the non-microvoid coalescence mode of fracture in the alloys in the temperature region of −140 to −77°C, a significant role of plastic strain in fracture is identified. The significance of the critical strain zone for fracture is discussed and it has been compared with the process zone at fracture.     

Investigation of loading rate and plate thickness effects on dynamic fracture toughness of PMMA

To investigate the effects of loading rate and plate thickness on the fracture toughness of PMMA (polymethyl methacrylate) under impact loading, two methods, A method and B method, are applied as follows. In the A method, a dynamic finite element method and a strain gage method are applied to measure the dynamic fracture toughness in the fracture test using an air gun. In the B method, a single axis strain gage method is applied to measure the critical dynamic stress intensity factor, namely dynamic fracture toughness, in the fracture test using a weight dropping type apparatus. The dimensions of the PMMA specimen are L = 140 mm length and W = 30 mm width. Three values of the plate thickness B, 15.0 mm, 10.0 mm and 5.0 mm, are selected to investigate the plate thickness effect in the fracture test. Both results by the A and B methods precisely indicated the minimum value and the loading rate effect on the dynamic fracture toughness.     

Dependence of the dynamic strength on loading rate

Document presented at the 1st All-Union Conference on Fracture Mechanics of Materials, Lvov, October 20–22, 1987.     

Polypropylene foam behaviour under dynamic loadings: Strain rate,density and microstructure effects

Expanded polypropylene foams (EPP) can be used to absorb shock energy. The performance of these foams has to be studied as a function of several parameters such as density, microstructure and also the strain rate imposed during dynamic loading. The compressive stress–strain behaviour of these foams has been investigated over a wide range of engineering strain rates from 0.01 to 1500 s⁻¹ in order to demonstrate the effects of foam density and strain rate on the initial collapse stress and the hardening modulus in the post-yield plateau region. A flywheel apparatus has been used for intermediate strain rates of about 200 s⁻¹ and higher strain rate compression tests were performed using a viscoelastic Split Hopkinson Pressure Bar apparatus (SHPB), with nylon bars, at strain rates around 1500 s⁻¹ EPP foams of various densities from 34 to 150 kg m⁻³ were considered and microstructural aspects were examined using two particular foams. Finally, in order to assess the contribution of the gas trapped in the closed cells of the foams, compression tests in a fluid chamber at quasi-static and dynamic loading velocities were performed.     

Strain rate effects on viscoelastic crack bifurcation

The effects of applied strain rate on the viscoelastic crack bifurcation phenomenon in Polymethyl Methacrylate (PMMA) were investigated. It was still verified that the product $\text{σ}{}_{\mathrm{f}}\text{C}{}_{\mathrm{b}}{}^{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}$ was constant, as was already observed by Congleton and Petch, and Anthony, Chubb and Congleton, for brittle elastic materials, for any strain rate, where σ_f = the gross fracture stress and C_b= the main crack length until the bifurcation starts. However, it was found that the higher strain rate increases the main crack length C_b resulting in the decrease in the gross fracture stress σ_f and vice versa. This might be interpreted that the higher stress concentration at the initiation crack tip, which is realized by becoming more brittle due to the higher strain rate owing to the predominance of the elastic element in the viscoelastic material, decreases the gross fracture stress leading to the longer main crack length.     

Effect of strength mis-match and dynamic loading on ductile fracture initiation

It has been well known that ductile fracture of steels is accelerated by triaxial stresses. The characteristics of ductile crack initiation in steels are evaluated quantitatively using a two-parameter criterion based on equivalent plastic strain and stress triaxiality.The present study focuses on the effects of geometrical discontinuity, strength mis-match, which can elevate plastic constraint due to heterogeneous plastic straining, and loading rate on the critical condition for ductile fracture initiation using a two-parameter criterion. Fracture initiation testing has been conducted under static and dynamic loading using circumferentially notched round-bar specimens. In order to evaluate the stress/strain state in the specimens, especially under dynamic loading, a thermal elastic-plastic dynamic finite element (FE) analysis considering the temperature rise due to plastic deformation has been carried out.The tensile tests on specimens with an undermatching interlayer showed that the relationship between the critical equivalent plastic strain to initiate ductile fracture and stress triaxiality was equivalent to that obtained on homogeneous specimens under static loading. Moreover, the two-parameter criterion for ductile fracture initiation is shown to be independent of the loading rate. It was demonstrated that the critical global strain to initiate ductile fracture in specimens with strength mis-match under various loading rate can be estimated based on the local criterion, that is two-parameter criterion obtained on homogeneous specimens under static tension, by mean of FE-analysis taken into account accurately both strength mis-match and dynamic loading effects on stress/strain behaviors.     

A criterion for dynamic fracture strength of materials

A phenomenological criterion for damage to materials due to short duration stresses is proposed. Based on the proposed criterion, an equation is obtained to find the time to failure corresponding to an applied stress history. It is shown that the equation is in agreement with several experimental and theoretical studies. The criterion is generalized to the case of repeated loading and an equation is derived to calculate cumulative damage under repeated loading. The predictions of the equation are in qualitative agreement with some test data.     

Limit velocity of fracture front and dynamic strength of brittle solids

The theories of propagation of brittle fracture fronts in solid materials are compared with experimental data. Instead of the well-known theory of the limit fracture stress the theory of limit velocity of fracture front is developed. Accordingly between the moving boundary at which the static strength is attained and the front of fracture the material can stand essential dynamic over-loadings. The experimental data on contained explosions in optically transparent intact blocks show that the limit velocity of brittle cracks front takes place immediately after the separation of the shock front and the front of brittle fracture. The hypothesis of the existence of limit front velocity leads to the conclusion that in the two-front structure of plane shock waves the amplitude of elastic precursors, known as “the Hugoniot elastic limit”, exceeds the value of ultimate static strength of a solid material and has to increase with increasing of a finite shock pressure. This effect is justified by a number of experiments with brittle materials. The analogue with the plane problem of a self-supporting brittle burst is shown. The explanation of exceeding of the ultimate static strength and of “the delay time” of fracture under the spall condition is given. The increasing of internal fractures, which is described by the dilatancy loosening of materials is discussed. The well-known laws of “the geometrical similarity” of contained explosions are in accordance with expression of the strength in terms of the ultimate stress but not in terms of Griffith's energy for creating of new cracks. The possibility of the regime of a limit front velocity of fracture at explosion motions in real rocks, for which the dilatancy has place, is discussed.     

Damage mode effects on fracture strength of ultra-high temperature ceramics

Improving the fracture strength of ceramics has been one of the most important concerns in the ceramics field, and highly accurate evaluation of the fracture strength of ceramics is the right foundation of this topic. In this paper, we analyze fracture strength by using a previously established temperature-damage-dependent strength model. Sensitivities of fracture strength to relative parameters are analyzed, and the influences of different failure modes and typical sizes of different micro-structural characteristics on the fracture strength of ultra-high temperature ceramics (UHTCs) are discussed. This study can provide a theoretical basis and technical platform for the design, application and reliability assessment of UHTCs in applications.     

Damage mode effects on fracture strength of ultra-high temperature ceramics

Improving the fracture strength of ceramics has been one of the most important concerns in the ceramics field, and highly accurate evaluation of the fracture strength of ceramics is the right foundation of this topic. In this paper, we analyze fracture strength by using a previously established temperature-damage-dependent strength model. Sensitivities of fracture strength to relative parameters are analyzed, and the influences of different failure modes and typical sizes of different micro-structural characteristics on the fracture strength of ultra-high temperature ceramics (UHTCs) are discussed. This study can provide a theoretical basis and technical platform for the design, application and reliability assessment of UHTCs in applications.     

Effect of loading rate on dynamic fracture initiation toughness of brittle materials

Numerical simulation is carried out to investigate the effect of loading rate on dynamic fracture initiation toughness including the crack-tip constraint. Finite element analyses are performed for a single edge cracked plate whose crack surface is subjected to uniform pressure with various loading rate. The first three terms in the Williams’ asymptotic series solution is utilized to characterize the crack-tip stress field under dynamic loads. The coefficient of the third term in Williams’ solution, A ₃, was utilized as a crack tip constraint parameter. Numerical results demonstrate that (a) the dynamic crack tip opening stress field is well represented by the three term solution at various loading rate, (b) the loading rate can be reflected by the constraint, and (c) the constraint A ₃ decreases with increasing loading rate. To predict the dynamic fracture initiation toughness, a failure criterion based on the attainment of a critical opening stress at a critical distance ahead of the crack tip is assumed. Using this failure criterion with the constraint parameter, A ₃, fracture initiation toughness is determined and in agreement with available experimental data for Homalite-100 material at various loading rate.     

Strain rate and temperature effects on energy absorption of polyethylene fibres and composites

The influence of strain rate and temperature on modulus, strength and work of fracture of high-performance polyethylene (HP-PE) fibres and composites is investigated. Results showed that an increase in strain rate and/or decrease in temperature leads to a reduction in work of fracture. At high strain rates or low temperatures a constant minimum level for the fracture energy is reached. The energy absorption capacity of HP-PE/epoxy laminates is investigated using full penetrating dart-impact tests and showed similar trends than observed for HP-PE fibres. The impact energy of these laminates could be described quantitatively in terms of fibre, matrix and delamination effects by combining the tensile test results on fibres and unidirectional composites with fracture toughness experiments on laminates.     

氧化铝陶瓷动态压缩强度的高压和高应变率效应

平面冲击压缩下材料由弹性到非弹性变形转变的临界值对应着材料的动态压缩强度,高压和高应变率强烈影响材料的强度。采用粘塑性比拟法建立了材料发生非弹性变形的动态屈服条件,并引入Drucker-Prager静态屈服准则,可以联合考虑动态压缩强度的高压和高应变率效应,据此提出了新的Hugoniot弹性极限表征形式。利用轻气炮进行了氧化铝陶瓷平板冲击实验,VISAR测试了样品的自由面速度历程,讨论了氧化铝陶瓷动态压缩强度的测定和存在的不确定性问题。     

Strain rate effects on the mechanical behavior of nanocrystalline Au films

The effect of fabrication, film thickness, and strain rate on the mechanical behavior of Au films with 100 nm (evaporated gold) and 200 nm (electroplated gold) average grain sizes was investigated. Uniaxial tension was imposed at 10^− 3-10^− 6 s^− 1 strain rates on evaporated 0.5 μm and 0.65 μm thick Au specimens, and at 10^− 2-10^− 5 s^− 1 on electroplated 2.8 μm thick Au specimens. Strain rates between 10^− 3 and 10^− 5 s^− 1 had a marked impact on the ultimate strain of evaporated films and less significant effect on their yield and saturation stress. The ductility increased with decreasing strain rate and it varied between 2-4.5% for 500-650 nm thick films and 3.4-10.6% for 2.8 μm thick films. When compared at the same strain rate, the thick electroplated films were more ductile than the thin evaporated films, but their yield and saturation stresses were lower, possibly due to their larger grain size. Qualitatively, the stress-strain behavior was consistent at all rates except at the slowest that resulted in significantly different trends. A marked decrease of the maximum strength, effective Young's modulus, and yield strength occurred at 10^− 6 s^− 1 for thin, and at 10^− 5 s^− 1 for thick films, while for 500 nm thin films multiple stress localizations per stress-strain curve were recorded. Because of temperature, applied stress, and grain size considerations this behavior was attributed to dislocation creep taking place at a strain rate comparable to the applied strain rate.     

R-curve modeling of rate and size effects in quasibrittle fracture

The equivalent linear elastic fracture model based on an R-curve (a curve characterizing the variation of the critical energy release rate with the crack propagation length) is generalized to describe both the rate effect and size effect observed in concrete, rock or other quasibrittle materials. It is assumed that the crack propagation velocity depends on the ratio of the stress intensity factor to its critical value based on the R-curve and that this dependence has the form of a power function with an exponent much larger than 1. The shape of the R-curve is determined as the envelope of the fracture equilibrium curves corresponding to the maximum load values for geometrically similar specimens of different sizes. The creep in the bulk of a concrete specimen must be taken into account, which is done by replacing the elastic constants in the linear elastic fracture mechanics (LEFM) formulas with a linear viscoelastic operator in time (for rocks, which do not creep, this is omitted). The experimental observation that the brittleness of concrete increases as the loading rate decreases (i.e. the response shifts in the size effect plot closer to LEFM) can be approximately described by assuming that stress relaxation causes the effective process zone lenght in the R-curve expression to decrease with a decreasing loading rate. Another power function is used to describe this. Good fits of test data for which the times to peak range from 1 sec to 250000 sec are demonstrated. Furthermore, the theory also describes the recently conducted relaxation tests, as well as the recently observed response to a sudden change of loading rate (both increase and decrease), and particularly the fact that a sufficient rate increase in the post-peak range can produce a load-displacement response of positive slope leading to a second peak.     

Strain rate and gage length effects on tensile behavior of Kevlar 49 single yarn

In the present paper, Kevlar® 49 single yarns with different gage lengths were tested under both quasi-static loading at a strain rate of 4.2 × 10^?4 s^?1 using a MTS load frame and dynamic tensile loading over a strain rate range of 20–100 s^?1 using a servo-hydraulic high-rate testing system. The experimental results showed that the material mechanical properties are dependent on gage length and strain rate. Young’s modulus, tensile strength, maximum strain and toughness increase with increasing strain rate under dynamic loading; however the tensile strength decreases with increasing gage length under quasi-static loading. Weibull statistics were used to quantify the degree of variability in yarn strength at different gage lengths and strain rates. This data was then used to build an analytical model simulating the stress–strain response of single yarn under dynamic loading. The model predictions agree reasonably well with the experimental data.     

Strain rate effects in concrete structures: The LCPC experience

This paper presents, first, a synthesis of the research work carried out at LCPC on the dynamic behaviour of concrete structures, and second, the studies which remain to be performed in response to professional needs.

The main advances of this research can be summarized as follows:

• -For strain rates less or equal to 1 s^?1, an increase in material strength is related to viscous phenomena due to the presence of free water in the nanopores of concrete hydrates. This increase is independent of the water/cement ratio of the concrete. For strain rates equal to or greater than 10 s^?1, inertia forces are mainly responsable for increasing strength.
• -Two numerical modellings are being implemented in the finite-element code CESAR-LCPC: the first is a visco-elastoplastic degrading model with viscous hardening; the second is a discrete probabilistic viscous cracking model. These models take into account the physical mechanisms observed and analyzed during the experimental studies.

Further experimental and theoretical studies of the dynamic behaviour of the rebar/concrete interface appear as a priority for the future.     

Strain rate and temperature dependence of tensile strength for carbon/glass fibre hybrid composites

The tensile strength of epoxy resin reinforced with a random planar orientation of short carbon and glass fibres increased as the strain rate increased, and the increase in tensile strength became slightly remarkable with increasing temperature. The strain rate-temperature superposition was held for each composite. The strain rate and temperature dependence of tensile strength of composites could be estimated based on the dependence of the mechanical properties of the matrix resin, the interfacial yield shear strength and the critical fibre length. The strain rate and temperature dependence of the tensile strength of the hybrid composite could be estimated by the additive rule of hybrid mixtures, using the strain rate and temperature dependence of the tensile strength of both composites. The experimental values at a higher rate were lower than the calculated values. It was hypothesized that this may have been caused by the ineffective fibres formed during preparation of the specimen.