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.     

Theoretical Analysis on the Measurement Errors of Local 2D DIC: Part II Assessment of Strain Errors of the Local Smoothing Method–Approaching an Answer to the Overlap Question

In this paper, the strain error of subset‐based two‐dimensional digital image correlation (DIC) is theoretically derived. Analytical solutions are provided to estimate the strain error. A dimensionless factor is proposed, namely the overlap magnifier, which reveals the dependency of the strain error on the DIC regularisation parameters, that is, subset size, step size and strain window size. The derived equations are validated numerically and experimentally. The estimated random strain error is in good accordance with the experimental data. The proposed derivation can be readily extended to stereo DIC.     

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.     

Double bridge circuit for self‐validated structural health monitoring strain measurements

In structural health monitoring (SHM) applications, sensor faults and structural damage need to be assuredly discriminated. A self‐diagnosis strain sensor operating in a continuous online SHM scenario is considered. The strain sensor is based on full electric resistance strain gauge Wheatstone bridges. The state of the art shows that such a sensor has not yet been developed. The loop current step response (LCSR) is a well‐known method to detect strain gauge debonding. However, applying the LCSR method to a full strain gauge Wheatstone bridge has some limitations analysed in this paper. To enable the use of the LCSR method in an online SHM scenario, the double bridge circuit is proposed in this work. Two new strain gauge debonding fault detection methods and a new debonding fault isolation method—based on the double bridge circuit measurements—are proposed and evaluated. Two new sensor fusion weighting approaches are also proposed and evaluated—to achieve strain gauge debonding fault tolerance on the double bridge circuit. The experimental results show that the proposed methods can detect, isolate, and tolerate a strain gauge grid debonding fault and can be applied in an online SHM self‐diagnosis sensor scenario.     

Simple and accurate four-node axisymmetric element

Based on the assumed strain method, a simple four-node axisymmetric solid element is introduced. The assumed strain field is carefully selected to preserve the correct rank of the element stiffness matrix and to achieve high accuracy. The strain field is developed in conjunction with orthogonal projections and no matrix inversions are needed. The coarse mesh accuracy in bending and in typical axisymmetric load cases is excellent even for nearly incompressible materials. The strain-driven format obtained is well suited for materials with non-linear stress–strain relations. Several numerical examples are presented where the excellent performance of the proposed simple element is verified. Copyright © 2006 John Wiley & Sons, Ltd.     

A new path‐dependent multiaxial fatigue model for metals under different paths

Based on the critical plane approach, a new path‐dependent multiaxial fatigue model in low‐cycle fatigue is proposed. The proposed model includes damage contribution from four sources: the normal strain amplitude, the shear strain amplitude on the critical plane, the hydrostatic mean strain and a new path‐dependent factor. The effect of mean strain is considered by the hydrostatic mean strain. The experimental data of 11 kinds of materials are used to demonstrate the effectiveness of this new model under both zero and non‐zero mean strain multiaxial loading path.     

A Macromechanical Damage Model of Fibrous Laminated Composites

A new model for the damage factor in terms of strain energy densities is derived and proposed. The damage factor values can be predicted directly from the stress–strain data using the aforementioned model. Moreover, an expression of crack density ratios in terms of total strain energy densities is inferred. Their validity has been shown by comparing their results with the limited experimental data. The proposed model compares well with the model and the experimental data of Voyiadjis performed on metal-matrix laminates. A new technique, used to predict reasonably the values of crack density ratios at any fiber orientation angle using measured data in the principal material directions, is also developed. Due to difficulties encountered in the evaluation of amount of damage in composite materials up to failure, especially, when using experimental techniques, it was shown that the proposed method for finding the damage factor and crack-density ratios is sufficient and gives reasonable predictions.     

A Novel Class of Strain Measures for Digital Image Correlation

We propose a novel class strain measures for use with digital image correlation (DIC). Whereas the traditional notion of compatibility (strain as the derivative of the displacement field) is problematic when the displacement field varies substantially because of either measurement noise or material irregularity, the proposed measure remains robust, well defined and invariant under rigid body motion. Moreover, when the displacement field is smooth, the classical and proposed strain measures are approximations of each other. We demonstrate, via several numerical examples, the potential of this new strain measure for problems with steep gradients. We also show how the non‐local strain provides an intrinsic mechanism for filtering high‐frequency content from the strain profile and so has a high signal to noise ratio. This is a convenient feature considering image noise and its impact on strain calculations.     

Development of shear locking‐free shell elements using an enhanced assumed strain formulation

The degenerated approach for shell elements of Ahmad and co‐workers is revisited in this paper. To avoid transverse shear locking effects in four‐node bilinear elements, an alternative formulation based on the enhanced assumed strain (EAS) method of Simo and Rifai is proposed directed towards the transverse shear terms of the strain field. In the first part of the work the analysis of the null transverse shear strain subspace for the degenerated element and also for the selective reduced integration (SRI) and assumed natural strain (ANS) formulations is carried out. Locking effects are then justified by the inability of the null transverse shear strain subspace, implicitly defined by a given finite element, to properly reproduce the required displacement patterns. Illustrating the proposed approach, a remarkably simple single‐element test is described where ANS formulation fails to converge to the correct results, being characterized by the same performance as the degenerated shell element. The adequate enhancement of the null transverse shear strain subspace is provided by the EAS method, enforcing Kirchhoff hypothesis for low thickness values and leading to a framework for the development of shear‐locking‐free shell elements. Numerical linear elastic tests show improved results obtained with the proposed formulation. Copyright © 2001 John Wiley & Sons, Ltd.     

Development of stress-modified fracture strain for ductile failure of API X65 steel

The present paper proposes ductile failure criteria in terms of true fracture strain (the equivalent strain to fracture) as a function of the stress triaxiality (defined by the ratio of the hydrostatic stress to the equivalent stress) for the API X65 steel. To determine the stress-modified fracture strain, smooth and notched tensile bars with four different notch radii are tested, from which true fracture strains are determined as a function of the notch radius. Then detailed elastic–plastic, large strain finite element analyses are performed to estimate variations of stress triaxiality in the tensile bars, which leads to true fracture strains as a function of the stress triaxiality, by combining them with experimental results. Two different failure criteria are proposed, one based on local stress and strain information at the site where failure initiation is likely to take place, and the other based on averaged stress and strain information over the ligament where ductile fracture is expected. As a case study, ligament failures of API X65 pipes with a gouge are predicted and compared with experimental data.     

离心钢管混凝土的等效本构关系

在现有离心钢管混凝土本构关系分析的基础上,将离心钢管混凝土简化为同一尺度的横观各向同性体,利用在弹性状态下应变能相等原理和弹塑性状态时应力—应变呈二次抛物线变化的假定,提出了离心钢管混凝土这种组合结构新的等效本构关系。实例分析表明,模型与试验结果吻合较好,且该本构关系能客观地反映了离心钢管混凝土构件的物理力学关系,为离心钢管混凝土结构进行数值分析奠定了基础。     

考虑应变路径的多轴低周疲劳寿命预测模型

通过分析材料在多轴非比例加载下产生附加强化的机理,该文以拉扭薄壁管试件为研究对象,分析了临界平面上的应变状态,并在此基础上以塑性应变能为控制参数定义表征多轴低周疲劳寿命对应变路径依赖性的非比例度。基于多轴疲劳临界损伤面原理,应用von-Mises 准则和本文定义的应变路径非比例度参数建立起能反映应变路径对非比例附加强化影响的多轴低周疲劳寿命预测模型。利用该模型预测08X18H10T 不锈钢、Ti-6Al-4V合金、S460N 钢和2.25Cr-1Mo 钢这4 种材料的多轴疲劳寿命,并与试验值进行比较。结果表明:该模型的预测结果与试验结果吻合良好,能同时适用于比例与非比例加载,预测精度较高,便于工程应用。