D. Rittel

On the conversion of plastic work to heat during high strain rate deformation of glassy polymers

It has long been known that the mechanical energy of plastic deformation tranforms partly into heat (ratio bint) which can cause noticeable temperature rise under adiabatic conditions. Less is known about the rate of conversion of these quantities (ratio bdiff ). High strain rate deformation of metals was recently investigated by Mason et al. (1994) and Kapoor and Nemat-Nasser (1998). The former investigated the rate ratio bdiff and observed a strain and strain rate dependence. The latter investigated bint and concluded it is constant and equal to 1. Temperature measurement was made using infrared techniques. We investigate the thermomechanical behavior of glassy polymers (PC) deformed at strain rates ranging from 5000 to 8000 s ˇ1 . The temperature is assessed using small embedded thermocouples whose applicability to transient measurements has been recently revisited (Rittel, 1998a). Our results show a definite dependence of both b factors on the strain and strain rate. We also observe that whereas the overall ratio (bint) of the converted energy remains inferior to 1 as expected, the rate ratio (bdiff ) may reach values superior to 1 at the higher strain rates. This original observation is rationalized in terms of a decrease of the stored energy of cold work which corresponds to the softening regime of the stress strain curve. This additional energy transforms into heat thus causing the observed values of bdiff . While the present observations apply to a glassy polymer, it can reasonably be assumed that they apply to the broader context of strain softening. ” 1999 Elseiver Science Ltd. All rights reserved.

A Shear-compression Specimen for Large Strain Testing

A new specimen geometry, the shear-compression specimen (SCS), has been developed for large strain testing of materials. The specimen consists of a cylinder in which two diametrically opposed slots are machined at 45° with respect to the longitudinal axis, thus forming the test gage section. The specimen was analyzed numerically for two representative material models, and various gage geometries. This study shows that the stress (strain) state in the gage, is three-dimensional rather than simple shear as would be commonly assumed. Yet, the dominant deformation mode in the gage section is shear, and the stresses and strains are rather uniform. Simple relations were developed and assessed to relate the equivalent true stress and equivalent true plastic strain to the applied loads and displacements. The specimen was further validated through experiments carried out on OFHC copper, by comparing results obtained with the SCS to those obtained with compression cylinders. The SCS allows to investigate a large range of strain rates, from the quasi-static regime, through intermediate strain rates (1–100 s−1), up to very high strain rates (2×104s−1 in the present case).

An investigation of dynamic crack initiation in PMMA

The recently developed compact compression specimen (CCS) — H integral technique is applied to the characterization of the dynamic fracture toughness of PMMA under transient loading. The forces and displacements on the boundaries of a cracked CCS are applied and determined using a Kolsky apparatus. The path-independent H-integral is thus calculated by forming a convolution product between experimental and reference data. The evolution of both the mode I and mode II stress intensity factors is determined by solving linear convolution equations. Therefore, the history of the stress intensity factors is assessed from the onset of loading until early crack propagation detected by a fracture gage. Dynamic fracture toughness is taken as the value of the mode I stress intensity factor at fracture time. Experimental results compare well with previously reported values while extending the range of applied loading rates. The fracture toughness is observed to increase markedly with the stress intensity rate. This observation is discussed in the light of fractographic examination showing the existence of a characteristic rough zone directly ahead of the notch-tip of dynamically fractured specimens.

Failure modes of electrospun nanofibers

Failure modes of electrospun polymer nanofibers are reported. The nanofibers have diameters in the range of 80–400 nm and lengths greater then several centimeters. The nanofibers fail by a multiple necking mechanism, sometimes followed by the development of a fibriliar structure. This phenomenon is attributed to a strong stretching of solidified nanofibers by the tapered accumulating wheel (electrostatic lens), if its rotation speed becomes too high. Necking has not been observed in the nanofibers collected on a grounded plate.

A method for dynamic fracture toughness determination using short beams

This paper deals with dynamic fracture toughness testing of small beam specimens. The need for testing such specimens is often dictated by the characteristic dimensions of the end product. We present a new methodology which combines experimentally determined loads and fracture time, together with a numerical model of the specimen. Calculations are kept to a minimum by virtue of the linearity of the problem. The evolution of the stress intensity factor (SIF) is obtained by convolving the applied load with the calculated specimen response to unit impulse force. The fracture toughness is defined as the value of the SIF at fracture time. The numerical model is first tested by comparing numerical and analytical solutions (Kishimoto et al., 1990) of the impact loaded beam. One point impact experiments were carried out on of commercial tungsten base heavy alloy specimens. The robustness of the method is demonstrated by comparing directly measured stress intensity factors with the results of the hybrid experimental-numerical calculation. The method is simple to implement, computationally inexpensive, and allows testing of large sample sizes, without restriction on the specimen geometry and type of loading.

Theoretical and experimental analysis of longitudinal wave propagation in cylindrical viscoelastic rods

Wave propagation in viscoelastic rods is encountered in many applications including studies of impact and fracture under high strain rates and characterization of the dynamic behavior of viscoelastic materials. For viscoelastic materials, both material and geometric dispersion are possible when the diameter of the rod is of the same order as the wavelength. In this work, we simplify the Pochhammer frequency equation for low and intermediate loss viscoelastic materials and formulate corrections for geometric dispersion for both the phase velocity and attenuation. The formulation is then experimentally veri7ed with measurements of the phase velocity and attenuation in commercial polymethylmethacrylate rods that are 12 and 6:4 mm in diameter. Without correcting for geometric dispersion, the usable frequency range for determining the phase velocity and attenuation for the 12 mm rod is about 20 kHz, and about 35 kHz for the 6: 4mm rod. Using the correction procedure developed here, it was possible to accurately determine the phase velocity and attenuation up to frequencies exceeding 55 kHz for the 12 mm rod and 65 kHz for the 6:4 mm rod. These corrections are applicable to many polymers and other viscoelastic materials. From thereon, the viscoelastic properties of the material can be determined over a wide range of frequencies. ? 2003 Elsevier Science Ltd. All rights reserved.

An investigation of the heat generated during cyclic loading of two glassy polymers. Part I: Experimental

A comparative study of hysteretic heating was carried out in commercial polymethylmethacrylate (PMMA) and polycarbonate (PC) specimens subjected to cyclic compressive loading. Both materials heat up upon cycling with a pronounced influence of the cycling frequency and the stress amplitude. Commercial PMMA is very sensitive to minor variations in the maximum applied stress, which does not exceed 0.45 times the yield strength of this material. The temperature rise is continuous throughout the test. The maximum temperature reached is of the order of the glass transition temperature (Tg), and often more. Failure is sudden and consists of localized bulging in the central part of the specimen. Commercial PC can be tested at much higher stress levels, of the order of its yield strength. Here, a welldefined temperature peak, which has not been reported previously, develops during the initial stage of the loading. The maximum temperature reached during the test does not exceed 0.8Tg. The sharpness of the peak improves with increasing stress amplitude and testing frequency. Failure of the specimen occurs by diAuse barreling. Annealing heat treatments shorten the fatigue life of PMMA specimens and decrease the sharpness of the thermal peak of PC specimens. A non-uniform temperature distribution is observed to develop in the specimen during cycling. Consequently, care should be paid to the thermal boundary conditions of the problem. The failure mechanism (diAuse vs. localized) of the investigated materials is thus dictated both by the temperature distribution and by the extent of the temperature rise. ” 2000 Elsevier Science Ltd. All rights reserved.

Large strain constitutive behavior of OFHC copper over a wide range of strain rates using the shear compression specimen

A new specimen geometry, the shear compression specimen (SCS), has been developed and validated for large strain testing of metals over a wide range of strain rates. A detailed numerical analysis of this specimen is presented to assess its range of applications and limitations. The dominant deformation mode of the gage section of the SCS is found to be shear. The stress and strain state in the gage section is necessarily three-dimensional, in contrast with commonly assumed situations of simple shear. Yet, considerable simplification is gained through the introduction of simple approximations for the Mises equivalent stress and plastic strain. These fields are found to be uniformly distributed over the gage section. The SCS framework is applied to the characterization of the large strain behavior of OFHC copper over a range of strain rates e_e = 10^(-3) to 3.2×10^4 s^(−1). The strain rate sensitivity of the material is noted, in accord with previous observations. The mechanical tests are complemented by microstructural characterization of the material which corroborate the numerical predictions of uniformity of the equivalent strain. The grains in the gage section are discernable for true strains less than 2. At larger strains, of the order of 3.5, the individual grains are no longer discernable and small equiaxed grains are observed, using scanning electron microscopy. These grains are characteristic of recrystallized material. The use of a single specimen geometry coupled to simple data reduction procedures is expected to promote constitutive characterization at large strains over a seamless range of strain rates.

An investigation of the heat generated during cyclic loading of two glassy polymers. Part II: Thermal analysis

This paper presents the thermal analysis of cyclic compression experiments which were carried out on commercial PC and PMMA cylindrical specimens. The thermal problem is solved numerically (finite element). Uniform internal heat generation is assessed from the experimental evolution of the hysteretic energy rate throughout the experiment. The results show a very good agreement between the calculated and the measured temperatures. The temperature peak which characterized the PC specimens and the continuously rising temperature of the PMMA cylinders are very well reproduced using simple assumptions of uniform heat generation and a constant ratio of the thermal to mechanical power conversion (ba 0:5). The mathematical solution provides information on the temperature distribution and its dependence on the boundary conditions (insulation of the specimen from the platens). These results are discussed with respect to surface temperature sensing of polymeric materials. ” 2000 Elsevier Science Ltd. All rights reserved.

Fragmentation of a porous viscoelastic material: Implications to magma fragmentation

Fragmentation of vesicular magma by rapid decompression is one of the most likely triggers for explosive eruptions. In this phenomenon the decompression rate and the viscoelastic nature of magma are considered to be key factors. In order to obtain a clear idea on the effects of these two factors, controlled fragmentation experiments have been conducted. These experiments have three advantages. First, the specimen is made of a viscoelastic material with controlled porosity and geometry. Second, the fragmentation process is directly monitored. Finally, both the magnitude and rate of decompression are controlled. Brittle fragmentation and ductile expansion were both observed in the same porous material at different timescales. The various mechanical responses of the specimen (elastic, flow, and fragmentation) were correlated with the pressure profile measured at the base of the specimen. Fragmentation was noted to occur when the decompression exceeded a critical value within a critical time. Two relevant timescales are discussed in terms of physical mechanisms of relaxation. The first is the measured glass transition time. The second is the estimated timescale for the onset of viscous bubble expansion. The observed phenomena bear several similarities with natural magma fragmentation. It is thus considered that the present results are a useful step toward constructing a model for magma fragmentation.