A novel approach to measure local strains in polymer matrix systems using polarised Raman microscopy

A novel approach to measure local strains in amorphous polymers is described. The method is based on the identification of changes in the molecular orientation with strain. Molecular orientation is quantified through a series expansion of Legendre functions where the coefficients of the series are determined from the Raman scattering intensities by varying the polarizations of incident and scattered light. The relations between the elements of the strain tensor and the coefficients of the Legendre functions are obtained from a set of simple uniaxial strain tests. The experimental technique is applied to measure the thermal strain field in the matrix around an embedded fibre in a single fibre model composite. The experimental results indicate that local shear yielding takes place within the matrix. This conclusion was supported by measurements of strain distribution in the fibre.     

An energy‐based damage parameter for the life prediction of AISI 304 stainless steel subjected to mean strain

Abstract

This study extends the plastic strain energy approach to predict the fatigue life of AISI 304 stainless steel. A modified energy parameter based on the stable plastic strain energy density under tension conditions is proposed to account for the mean strain and stress effects in a low cycle fatigue regime. The fatigue life curve based on the proposed energy parameter can be obtained directly by modifying the parameters in the fatigue life curve based on the stable plastic strain energy pertaining to fully reversed cyclic loading. Hence, the proposed damage parameter provides a convenient means of evaluating fatigue life on the mean strain or stress effect. The modified energy parameter can also be used to explain the combined effect of alternating and mean strain/stress on the fatigue life. In this study, the mean strain effects on the fatigue life of AISI 304 stainless steel are examined by performing fatigue tests at different mean strain levels. The experimental results indicate that the combination of an alternating strain and a mean strain strongly influences the fatigue life. Meanwhile, it is found that the change in fatigue life is sensitive to changes in the proposed damage parameter under the condition of a constant strain amplitude at various mean strain levels. A good agreement is observed between the experimental fatigue life and the fatigue life predicted by the proposed damage parameter. The damage parameter proposed by Smith et al. (1970) is also employed to quantify the mean strain effect. The results indicate that this parameter also provides a reasonable estimate of the fatigue life of AISI 304 stainless steel. However, a simple statistical analysis confirms that the proposed damage parameter provides a better prediction of the fatigue life of AISI 304 stainless steel than the SWT parameter.     

Structural fatigue crack growth on a representative volume element under cyclic strain behavior

By introducing parameters λ and ω into the crack tip field, a unified cyclic stress and strain field was first formulated by using the Hutchinson-Rice-Rosengren (HRR) field and the Rice-Kujawski-Ellyin (RKE) field under plane stress states in the present study. On the basis of the plastic strain energy and the linear damage accumulation, two fatigue crack growth models without any artificial parameters were then proposed from a representative volume element of cyclic strain behavior. The fatigue crack growth model included parameters λ and ω which showed the effect of two singularity fields. In addition, a simplified structural fatigue crack growth model was eventually established in terms of the fatigue life of each point on the crack front and the non-self-similar shape evolution law. Finally, the predictions of models are compared with the experimental data and the agreement is found to be fairly good.     

A Probabilistic Evaluation of the Least Squares Strain Tensor Derived from a Three-Dimensional Modular Strain Rosette Using the Monte-Carlo Technique

Abstract:  Strain gradients give rise to a number of problems in the field of embedded three-dimensional strain measurement. In order to avoid these problems a modular type three-dimensional strain rosette was embedded into known strain fields and the data from the individual gauges compared with theoretical predictions. Finally, the least squares strain tensor was predicted from experimental data analysed using the Monte-Carlo technique and the theoretical results forecast from finite element data taking into account the mechanical properties of the carrier, plug and prismatic bar. Some of the experimental results were found to correlate well with the theoretical values but some values in the least squares strain tensor, in particular under compression and torsional loading, departed considerably from the theoretical values. It was found that the effect of the measurement errors in the individual gauges combined with the matrix operations in the least squares strain tensor were responsible for biasing the resultant tensor data. However, the modular technique provided a solution to the problem of strain gradients.     

A comparison of three‐dimensional embedded strain transducers,compression tested within the same strain field while offset at an angle with the principal axes

Abstract: The strain tensor and principal strains were derived for a range of different patterns of three‐dimensional strain transducers. The precisions of the estimates of these values were based on the Monte Carlo simulation applied to experimental work that was conducted on strain transducers tested within the same strain field. The estimates of precision were also determined theoretically and compared with results based on experimental findings. Results suggest that the tetrahedron transducers in experimental work do not perform as well as rectangular patterns and that estimates of principal strains, which were not coincident with the axes of the transducer, showed slight discrepancies.     

Implicit algorithm for finite deformation hypoelastic–viscoplasticity in fcc metals

An implicit objective stress update algorithm is proposed for a hypoelastic–viscoplastic model. A thermal/dynamic yield function, which is derived based on the thermal activation analysis and dislocation interaction mechanisms, is used, along with the Consistency approach and the framework of additive viscoplasticity, in deriving the proposed model for fcc metals. The corotational formulation approach is utilized in developing the proposed model in the finite deformation field. For the case of the Newton–Raphson iteration method, a new expression for the consistent (algorithmic) tangent stiffness matrix of rate‐dependent metals is derived by direct linearization of the stress update algorithm. Finite element simulations are performed by implementing the proposed viscoplasticity constitutive models in the commercial finite element program ABAQUS. Numerical implementation for a simple tensile problem is used for validating the material parameters of the OFHC Copper under low and high strain rates and temperatures. The numerical results of the adiabatic true stress–true strain curves compare very well with the experimental data. The effectiveness of the present approach is tested by studying strain localization in a simple plane strain problem. Results indicate excellent performance of the present framework in describing the strain localization problem and in obtaining mesh‐independent results. Copyright © 2006 John Wiley & Sons, Ltd.     

A Novel Strain Sensor for Reinforced Concrete Structures

Abstract:  Reinforced concrete (RC) is the most commonly used structural material in civil engineering applications. RC structures have long-term service lives under normal loading conditions; however, overload caused by misuse or statistically remote events such as earthquakes may create damages that, if not detected in time, may eventually cause failure. Hence, it is important to monitor RC structures to take necessary precautions and save human lives. A long-gauge strain (LGS) sensor has been developed to monitor these structures. While it has been developed mainly with concrete applications in mind, the new sensor can also be used in a variety of applications, including measuring strains in pipelines, steel structures, and the like. The proposed sensor system has a very low cost compared with the commercially available competing systems. Prototypes of the proposed strain sensors have been built and calibrated. Test results prove the accuracy, repeatability and reliability of the proposed strain sensor. When the LGS sensor was incorporated into a concrete beam there was very good agreement between the experimental measurement of strain using the LGS sensor when compared with two strain-gauged parallel steel rebars in the same concrete beam.     

Interface crack problems with strain gradient effects

In this paper, the strain gradient theory proposed by Chen and Wang (2001a, 2002b) is used to analyze an interface crack tip field at micron scales. Numerical results show that at a distance much larger than the dislocation spacing the classical continuum plasticity is applicable; but the stress level with the strain gradient effect is significantly higher than that in classical plasticity immediately ahead of the crack tip. The singularity of stresses in the strain gradient theory is higher than that in HRR field and it slightly exceeds or equals to the square root singularity and has no relation with the material hardening exponents. Several kinds of interface crack fields are calculated and compared. The interface crack tip field between an elastic-plastic material and a rigid substrate is different from that between two elastic-plastic solids. This study provides explanations for the crack growth in materials by decohesion at the atomic scale.     

The Reinforcement Effect of Strain Gauges Embedded in Low Modulus Materials

The reinforcement effect of electrical resistance strain gauges is well‐described in the literature, especially for strain gauges installed on surface. This paper considers the local reinforcement effect of strain gauges embedded within low Young modulus materials. In particular, by using a simple theoretical model, already used for strain gauges installed on the surface, it proposes a simple formula that allows the user to evaluate the local reinforcement effect of a generic strain gauge embedded on plastics, polymer composites, etc. The theoretical analysis has been integrated by numerical and experimental analyses, which confirmed the reliability of the proposed model.     

Strain Measurement on Composites: Errors due to Rosette Misalignment

Abstract: Electrical resistance strain gauges are increasingly used for the determination of the strain field in composite components. The effect of the angular misalignment of a strain gauge rosette on the determination of the strains in a composite material is investigated in this paper. The theoretical analysis shows that the strain error along the principal material directions depends on the difference of principal strains, on the angular misalignment of the rosette and on the angle between the maximum principal strain and the fibre direction. The paper also shows experimental evidence for the theoretical analysis.