Off-axis Tension Tests Research Articles

Some improvements on Sun–Chen’s one-parameter plasticity model for fibrous composites – Part I: Constitutive modelling for tension–compression asymmetry response

Herein, a one-parameter plasticity model proposed by Sun and Chen [Sun CT and Chen JL. A simple flow rule for characterizing nonlinear behavior of fiber composites. J Compos Mater 1989; 23: 1009–1020] demonstrates features that make it highly attractive for characterizing non-linear responses of fibrous composites. However, a detailed exploitation of the model’s potential has been halted by unresolved problems that include tension–compression asymmetry in stress–strain curves, FEM implementation as well as optimal parameters determination, which are addressed in this investigation as well as proposed solutions are presented. The major focus in Part I of this three-part study was devoted to developing a simple model for predicting the tension–compression asymmetry in stress–strain curves for fibrous composites, which was based on Sun and Chen’s one-parameter plasticity model. A generalized Hill yield criterion was proposed from combinations of the Drucker–Prager yield criterion that considers the effect of hydrostatic pressure for isotropic materials and the Hill yield criterion suitable for anisotropic materials. By incorporating the yield strength-differential effect on the plastic flow rule in composite laminates, the one-parameter plasticity model was extended to a strength-differential effect-incorporated model. The improved model has been calibrated and validated by off-axis tension and compression tests on unidirectional carbon/epoxy (IM600/Q133) composite laminates. Results verified that the proposed model captured the complex tension–compression asymmetry in observed non-linear responses of stress–strain curves.

Evaluate orthotropic properties of wood using digital image correlation

The goal of this study is to evaluate the orthotropic properties of four different wood species. Off-axis tension tests with digital image correlation were used to evaluate the orthotropic properties of Larix kaempferi, Pinus densiflora, Pinus koraiensis, and Cryptomeria japonica. The highest elastic modulus EL of 11.70GPa was found from Larix kaempferi, whereas the lowest elastic modulus ER of 0.12GPa was observed from Cryptomeria japonica. The highest shear modulus GLT of 2.68GPa was found from Larix kaempferi and the lowest shear modulus GLR of 0.32GPa was observed from Cryptomeria japonica. While the shear modulus values in the LT plane from the four species were higher, the shear strength values in the LR plane were higher than those in the LR plane. Poisson’s ratios from the four species were found that νRT and νTR were higher than νLR and νLT. Although mixed failure behaviors were found from the four species, the failure behaviors were dominantly influenced by the orientation of the specimens.

Damage characteristics and constitutive modeling of the 2D C/SiC composite: Part I – Experiment and analysis

This paper reports an experimental investigation on the macroscopic mechanical behaviors and damage mechanisms of the plain-woven (2D) C/SiC composite under in-plane on- and off-axis loading conditions. Specimens with 15°, 30°, and 45° off-axis angles were prepared and tested under monotonic and incremental cyclic tension and compression loads. The obtained results were compared with those of uniaxial tension, compression, and shear specimens. The relationships between the damage modes and the stress state were analyzed based on scanning electronic microscopy (SEM) observations and acoustic emission (AE) data. The test results reveal the remarkable axial anisotropy and unilateral behavior of the material. The off-axis tension test results show that the material is fiber-dominant and the evolution rate of damage and inelastic strain is accelerated under the corresponding combined biaxial tension and shear loads. Due to the damage impediment effect of compression stress, compression specimens show higher mechanical properties and lower damage evolution rates than tension specimens with the same off-axis angle. Under cyclic tension–compression loadings, both on-axis and off-axis specimens exhibit progressive damage deactivation behaviors in the compression range, but with different deactivation rates.

A new stress-based multi-scale failure criterion of composites and its validation in open hole tension tests

A new stress-based multi-scale failure criterion is proposed based on a series of off-axis tension tests, and their corresponding fiber failure modes and matrix failure modes are determined at the microscopic level. It is a physical mechanism based, three-dimensional damage analysis criterion which takes into consideration the constituent properties on the macroscopic failure behavior of the composite laminates. A complete set of stress transformation, damage determination and evolution methods are established to realize the application of the multi-scale method in failure analysis. Open-hole tension (OHT) specimens of three material systems (CCF300/5228, CCF300/5428 and T700/5428) are tested according to ASTM standard D5766, and good agreements are found between the experimental results and the numerical predictions. It is found that fiber strength is a key factor influencing the ultimate strength of the laminates, while matrix failure alleviates the stress concentration around the hole. Different matchings of fiber and matrix result in different failure modes as well as ultimate strengths.

In-plane shear strength of paper measured by asymmetric four-point bending test

Abstract The in-plane shear strengths (IPSS) of copy paper, filter paper, and sack paper were obtained from an asymmetric four-point bending (AFPB) test. Rectangular tabs of medium-density fibreboard (MDF) were bonded to the paper specimen. The length of the clearance between the tabs was varied, and the influence of the clearance on the IPSS value was investigated. The IPSS obtained from the AFPB test was compared with that obtained from a 35° off-axis tension (OAT) test, which was proposed in a previous study. The IPSS values obtained from the AFPB tests on the copy paper and sack paper were significantly lower than those obtained from the 35° OAT tests because of the localised buckling caused by the negative principal stress. In contrast, the IPSS values obtained from the AFPB and OAT tests on the filter paper were in agreement when the clearance length was >5 mm because the buckling effect was excluded.

Failure analysis of typical glubam with bidirectional fibers by off-axis tension tests

Glubam is a new construction material using laminated bamboo with bidirectional fibers. In this paper, we present the failure analysis of glubam with bidirectional fibers using Hankinson formula and Tsai–Wu failure criterion. Off-axis tension tests were performed on glubam specimens with longitudinal to transverse fiber ratio of 4:1. The glubam specimens were designed to study its tensile properties in different directions to the main fiber. A revised Hankinson equation suitable for glubam are developed yielding satisfactory agreement with the test results. It is found that the interaction coefficient F12 in Tsai–Wu failure theory can only be established from the 15° off-axis tension test. Also, three approximation methods, Tsai–Hill, “Hoffman”, and “Mises–Hencky” methods, are applied to estimate the value of interaction F12. Four failure envelopes of glubam have been presented and compared. By comparing with off-axis test data, the failure envelope from Tsai–Wu theory provides unconservative prediction when in-plane shear is ignored. Even when in-plane shear is considered, the failure envelope obtained from Tsai–Wu theory is still deemed unsuitable to represent the behavior of glubam. Therefore, it seems the empirical approach is currently appropriate to represent the behavior of the 4:1 glubam subjected to biaxial tensile stress state.

High strain rate in-plane shear behavior of composites

Studies are presented on in-plane shear properties of a typical plain weave E-glass/epoxy composite under high strain rate loading. In-plane shear properties were determined with ±45 degree off-axis compression and tension tests using a split Hopkinson pressure bar apparatus. In-plane shear properties are presented as a function of axial and shear strain rates. The range of axial strain rates for off-axis compression tests was 819–2003 per sec, and for off-axis tension tests was 91–180 per sec, whereas the range of shear strain rates for off-axis compression tests was 1388–3442 per sec and for off-axis tension tests was 153–303 per sec. In general, it was observed that in-plane shear strength was enhanced at high strain rate loading compared to that at quasi-static loading. Also, it was observed that in-plane shear strength increased with increasing strain rate within the range of strain rates considered.

On and off-axis tension behavior of fiber reinforced polymer composites incorporating multi-walled carbon nanotubes

This investigation experimentally examines the role of multi-walled carbon nanotubes (MWCNTs) on the tension (on-axis tension test) and in-plane shear (off-axis tension test) behaviors of carbon fiber reinforced polymer composites. Both pristine and chemically functionalized MWCNTs were utilized with four different loadings: 0.1, 0.5, 1.0, and 1.5 wt% of epoxy. Our investigation showed that with 1.5 wt% functionalized MWCNTs, failure strain, ultimate strength, and toughness of the off-axis tension test are improved by 39%, 51%, and 121%, respectively. On the contrary, limited improvements were observed for the on-axis tested samples with functionalized or pristine MWCNTs.

Modeling of Tension-Compression Asymmetry in Off-axis Nonlinear Rate-dependent Behavior of Unidirectional Carbon/Epoxy Composites

A phenomenological anisotropic theory of viscoplasticity that takes account of the difference between the nonlinear rate-dependent behaviors of unidirectional carbon fiber-reinforced composites under off-axis tensile and compressive loading conditions is presented. The plane-stress representation of the effective stress associated with the pressure-modified Hill’s anisotropic yield criterion is modified into a new form that allows consideration of the difference between the shear flow stress levels under transverse tension and compression, i.e., a shear flow differential effect, as well as of the difference between the transverse tensile and compressive flow stress levels, i.e., a transverse flow differential effect. The shear flow differential effect is modeled in two ways by assuming the sensitivity and insensitivity to transverse stress, respectively. The rate-dependent plastic deformation of unidirectional composites is modeled on the basis of the concept of overstress and the irreversible thermodynamics with internal variables. The viscoplasticity model proposed in the present study can be reduced to the form developed in an earlier study, which facilitates identification of material constants and comparison with other existing theories. Validity of the proposed viscoplasticity model is evaluated by comparing with the off-axis tension and compression test results on a unidirectional carbon/epoxy composite at different strain rates. It is demonstrated that consideration of both the transverse and shear flow differential effects is crucial for accurate prediction of the different nonlinear rate-dependent behaviors of unidirectional composites under off-axis tensile and compressive loading conditions and those two kinds of flow differential effects have successfully been modeled in the proposed theory of viscoplasticity.

一方向複合材料の非主軸試験方法の新提案

This paper presents the proposal of a new integrated method for off-axis tension and compression test in the unidirectional composites, and its application to the testing of in-plane shear characterization. To accomplish this goal, a new rotating-type end grip apparatus which installed a set of bearing that can load with the both directions of axial and radial in the hydraulic grips has been developed. The improved effect for the nonuniform stresses in the off-axis specimen was compared with the existing two different end grip systems. The results of numerical and experimental investigation were shown that this method is equal excelling with the conventional system with an oblique end-grip. It was also found that the new testing method is suitable for in-plane shear characterization and it is recommended that it should be considered as a possible testing method for the off-axis characterization in two load systems, tension and compression.

Plastic Anisotropy of A2024BE-T6 and O Aluminum Alloys

Multiaxial stress tests were carried out on thin-walled cylindrical specimens of the A2024BE-T6 alloy aged at 120°C for 1 hr and the A2024BE-O alloy fully annealed at 495°C for 1hr. The shear strength of these alloys is much lower than the tensile one, and the equi-strain surfaces in the tension-torsion stress field lie within Tresca's criterion. Planar anisotropy was determined from two types of multiaxial stress tests by means of the combined loading of axial load, internal pressure and torsion, referred to as “off-axis tension test” and “off-axis torsion test”. The degree of anisotropy is expressed by using two different measures : one is the proof stress and the other is the angle deviation between the directions of the principal stress (or principal shear stress) and principal strain increment (or principal shear strain increment). The A2024BE-T6 alloy exhibits more severe anisotropy than the A2024BE-O alloy and both alloys reveal more severe anisotropy in off-axis tension test than in off-axis torsion test. The plastic deformation behavior can be analyzed precisely by the constitutive equation derived from the anisotropic yield function, hardening law and associated flow rule.

Formulation of a Viscoplasticity Model for Unidirectional Carbon Fiber-Reinforced Composites with Differences in Off-Axis Tensile and Compressive Behaviors

Formulation of a phenomenological viscoplasticity model that accounts for differences in tensile and compressive nonlinear rate-dependent behaviors of unidirectional carbon fiber-reinforced composites in a given off-axis direction is attempted. Effective stress and effective viscoplastic strain for transversely isotropic materials are derived from a three-dimensional pressure-modified Hill's anisotropic yield criterion, and they are reduced to the forms for plane state of stress. A plane-stress viscoplasticity model furnished with a capability to predict the phenomena raised above is formulated on the basis of the concept of overstress and the irreversible thermodynamics with internal variables. A shear constraint parameter, in which the influence of the compressive transverse stress on the shear flow resistance is reflected, is taken into account in defining a modified form of effective viscoplastic strain rate to enhance the predictive capability of the viscoplasticity model. The viscoplasticity model discussed in the present study is designed so as to be reduced to the viscoplasticity model of the Gates-Sun type developed in the previous study, which allows easy identification of material constants. Validity of the proposed viscoplasticity model is evaluated by comparing with results of off-axis tension and compression tests on a unidirectional carbon/epoxy composite at different strain rates.

一方向ＣＦＲＰおよびＧＦＲＰのねじり挙動

The helicopter bearingless rotor flexbeam is usually made of glass-fiber reinforced plastic composite (GFRP). For improving performance and reliability as well as the reduction of maintenance cost and weight, CFRP is expected to be applied to the flexbeam of the rotor system in future. However, few researches regarding torsion behavior of unidirectional CFRP have been made. In this study, torsion behavior of unidirectional CFRP and GFRP was examined in detail. A two-axis tension/ torsion examination device was used to observe torsion behavior of CFRP and GFRP. It was confirmed that the behavior of such materials is comprised of linearity/non-linearity domains. In addition, off-axis tension tests were performed in order to explain a non-linear behavior with a one-parameter plasticity model proposed by Sun et al., and a plasticity parameter for each of the materials was obtained. A prediction of a linear/non-linear behavior also became possible by incorporating the 3-D plasticity model into an FEM analysis with the estimated plastic parameters. The torsional rigidities of CFRP and GFRP are almost the same. This suggests that GFRP can be replaced by CFRP as torsional elements of a helicopter flex beam without an increase in torsion torque of the rotor system.

Simple constitutive model for nonlinear response of fiber-reinforced composites with loading-directional dependence

Polymeric composites generally exhibit different nonlinear response in tension and compression tests. In this study, Sun and Chen’s one-parameter plasticity model [Sun C.T. and Chen J.L., 1989. A simple flow rule for characterizing nonlinear behavior of fiber composites, J Compos Mater 29, 457–463] is extended to incorporate the loading-directional dependence on the plastic flow in composite laminates. Off-axis specimens of unidirectional carbon/epoxy composites were tested in compression and tension. Based on experimental results of compression tests, a simple two-parameter constitutive model for characterizing nonlinear mechanical behavior of fiber-reinforced composites was established. Finally, comparison of model predictions with experimental results of off-axis tension tests indicated a good correlation between the two. The developed simple plasticity model can explain the difference of nonlinear response in tension and compression tests.

A multiscale mechanics approach for modeling textured polycrystalline thin films with nanothickness

A multiscale method is proposed for calculating elastic constants of textured polycrystalline thin films of nanothicknesses. In this method the molecular simulation and finite element method are hierarchically employed. The elastic constants for each single crystal are first calculated through the simulations of on- and off-axis tension tests of the single crystal using molecular statics. Subsequently, the constitutive relations for the single crystal are used in conjunction with a finite element code to study the macro-mechanical deformation and stresses in textured polycrystalline nanofilms. The result indicates that both film thickness and grain size influence the macro-Young's modulus and Poisson's ratio of the nanofilm. Specifically, for nickel, the value of the macro-Young's modulus decreases as film thickness decreases and increases as grain size decreases. The value of the macro-in-plane Poisson's ratio increases as the thickness decreases or grain size increases.

New Considerations on the Stress Field in an Off-axis Tensile Test

Two new analytical approaches are proposed for the off-axis tension test problem. Both of them are based on the Second Castigliano’s theorem. In the first one, a simple stress field that satisfies equilibrium conditions is used. In the second approach, integration constants of the stress field obtained by Pagano and Halpin are calculated directly, without the use of the displacement field. The first approach shows the points of maximum normal and shear stresses in a qualitative manner. The second approach, besides the fulfilment of equilibrium and compatibility conditions, minimizes the strain energy. Furthermore, both approaches give the same solution for bending moments and shear forces at specimen ends caused by coupling effects. After analyzing the stresses at critical points in the principal material directions, it is shown that the value of in-plane shear strength is usually underestimated. The effect of end constraints on the obtention of in-plane shear modulus is also analyzed.

The effect of hydrostatic pressure on the mechanical properties of glass fibre/epoxy unidirectional composites

An investigation has been carried out to show the effect of hydrostatic pressure up to 850 MPa on the mechanical properties of pure epoxy and unidirectional (UD) E glass/epoxy lamina. Longitudinal tension, transverse compression and 10° off-axis tension tests were carried out on the composites and compression tests were carried out on the resin. Strain gauges were used to measure the strains during tests at pressures up to 500 MPa. From the longitudinal tensile tests on UD lamina, the longitudinal tensile Young's modulus was found to increase slightly with increasing pressure, while the longitudinal tensile strength was found to fall, with a change in failure mode from axial splitting to a transverse break at elevated pressures. From the transverse compression tests on UD lamina, the transverse compressive Young's modulus and transverse compressive strength were both found to increase markedly with pressure. A knee in behaviour was seen in the transverse compressive strength at a pressure of about 300 MPa: below this pressure the failure appeared flaw dominated, while above this pressure the failure appeared yield dominated. The in-plane UD lamina shear strength, determined from the 10° off-axis tension tests, showed a similar behaviour to the transverse compression tests, with a transition in the failure behaviour at a pressure of around 300 MPa. Compression tests on pure epoxy samples showed that the compressive Young's modulus increased significantly with increasing pressure whilst the compressive strength showed a modest increase with increasing pressure. By using a micromechanical model and the measured pressure dependence of the epoxy resin, it was found that the pressure dependent increase in the transverse modulus for a UD lamina could be predicted accurately.

The effect of hydrostatic pressure on the mechanical properties of glass fibre/epoxy unidirectional composites

Abstract An investigation has been carried out to show the effect of hydrostatic pressure up to 850 MPa on the mechanical properties of pure epoxy and unidirectional (UD) E glass/epoxy lamina. Longitudinal tension, transverse compression and 10° off-axis tension tests were carried out on the composites and compression tests were carried out on the resin. Strain gauges were used to measure the strains during tests at pressures up to 500 MPa. From the longitudinal tensile tests on UD lamina, the longitudinal tensile Young's modulus was found to increase slightly with increasing pressure, while the longitudinal tensile strength was found to fall, with a change in failure mode from axial splitting to a transverse break at elevated pressures. From the transverse compression tests on UD lamina, the transverse compressive Young's modulus and transverse compressive strength were both found to increase markedly with pressure. A knee in behaviour was seen in the transverse compressive strength at a pressure of about 300 MPa: below this pressure the failure appeared flaw dominated, while above this pressure the failure appeared yield dominated. The in-plane UD lamina shear strength, determined from the 10° off-axis tension tests, showed a similar behaviour to the transverse compression tests, with a transition in the failure behaviour at a pressure of around 300 MPa. Compression tests on pure epoxy samples showed that the compressive Young's modulus increased significantly with increasing pressure whilst the compressive strength showed a modest increase with increasing pressure. By using a micromechanical model and the measured pressure dependence of the epoxy resin, it was found that the pressure dependent increase in the transverse modulus for a UD lamina could be predicted accurately.

Determination of the shear modulus of orthotropic materials from off-axis tension tests

The paper is concerned with the study of the possibility to determine the shear modulus of orthotropic materials using testing under tension in the direction making some angle with the principal material axis. Conditions that should be imposed on the material properties providing the possibility of this test are derived and analyzed in application to composite materials.

일 방향 탄소섬유 강화 알루미늄 적층 복합재료의 전단물성치 측정에 관한 연구

In order to study the effects of oblique tabs on the in-plane shear properties of unidirectional carbon fiber reinforced aluminum laminate composites, the l0°off-axis tensile test, the 45°off-axis tensile test and Iosipescu shear test were performed to determine the shear properties. Off-axis tension test was studied by using new oblique-shaped tabs proposed by Sun and Chung.^(7) Iosipescu shear test was studied by using modified Wyoming test fixture. The oblique tabs reduced remarkably end-constraint effects of off-axis specimens with a aspect ratio of about eight. The experimental results show that there is no significant difference between off-axis test results and those of Iosipescu shear test. Thebr/ 45°off-axis tensile tests are recommended for the determination of the shear properties of unidirectional carbon fiber reinforced aluminum laminated composites.br/