Semi‐empirische Berechnungsmethode zur Bestimmung des Grenzformänderungsdiagramms auf Basis mechanischer Kennwerte

Semi‐empirical calculation method for prediction of Forming Limit Curves based on mechanical properties For characterisation purposes of sheet metal forming processes concerning feasibility of material mainly the Forming Limit Curve (FLC) is commonly used. This failure model can either be measured experimentally or can be predicted by using semi‐empirical approaches. These mathematical approaches mainly are validated for Mild Steels. However, prediction of FLCs for modern High Strength Steels or Aluminium sheet alloys is not possible with acceptable accuracy today. This is why this contribution deals with a new semi‐empirical approach for FLC prediction, which is valid for all sheet metal materials used in car body production. This approach uses a correlation of mechanical properties of uniaxial tensile test an experimentally determined limit strains.     

Evaluation of non-linear strain paths using Generalized Forming Limit Concept and a modification of the Time Dependent Evaluation Method

The prediction of formability is one of the most important tasks in sheet metal forming process simulation. The common criterion for ductile fracture in industrial applications is the Forming Limit Diagram (FLD). This is only applicable for linear strain paths. However, in most industrial simulation cases non-linear strain paths occur. To resolve this problem, a phenomenological approach is introduced, the so-called Generalized Forming Limit Concept (GFLC). The GFLC enables prediction of localized necking on arbitrary non-linear strain paths. Another possibility is the use of the Time Dependent Evaluation Method (TDEM) within the simulation as a failure criteria. During the Numisheet Benchmark 1 (2014) a two-stage forming process was performed with three typical sheet materials (AA5182, DP600 and TRIP 780) and three different blank shapes. The task was to determinate the point in time and space of local instability. Therefore the strain path for the point of maximum local thinning is evaluated. To predict the start of local necking the Generalized Forming Limit Concept (GFLC), the Time Dependent Evaluation Method (TDEM) and the modified TDEM were applied. The results of the simulation are compared with the results of the Benchmark experiment.     

Improving the prediction of tensile failure in unidirectional fibre composites by introducing matrix shear yielding

A Monte Carlo simulation is established to predict the failure strain of unidirectional fibre composites. The effect of matrix shear yielding of a high performance epoxy resin is introduced into the model through load sharing factors between the fibres adjacent to fibre-break(s). Strain concentration factors (SCF) of fibres are obtained using Finite Element Methods (FEM) in a three dimensional multi-fibre unit cell containing one, two and three adjoining fibre-break(s). The tensile strains of the surviving adjacent fibres are intensified as a function of their distances from the fracture. A statistical simulation is carried out to predict the failure strain of a single layer of unidirectional (UD) fibre composites with the thickness of the fibre ineffective length. Using the weakest link theory, the ultimate failure strain of a real size UD composite is predicted.     

Constitutive modeling and the effects of strain-rate and temperature on the formability of Ti–6Al–4V alloy sheet

The constitutive model considering the strain-rate and temperature effects was presented by fitting the true stress–strain curves of Ti–6Al–4V alloy over a wide range of strain-rates (0.0005–0.05 s⁻¹) and temperatures (923–1023 K). The Forming Limit Curve (FLC) of Ti–6Al–4V alloy at 973 K was measured by conducting the hemispherical dome test with specimens of different widths. The forming limit prediction model of Ti–6Al–4V alloy, which takes strain-rate and temperature sensitivity into account, was predicted based on Marciniak and Kuczynski (M–K) theory along with Von Mises yield criterion. The comparison shows that the limit strain decreases with temperature lowering but strain-rate increasing. The comparison between theoretical analysis and experiment of FLC verifies the accuracy and reliability of the proposed methodology, which considers the strain-rate and temperature effects, to predict limit strains in the positive minor strain region of Forming Limit Diagram (FLD).     

Unidirectional carbon fibre reinforced polyamide-12 composites with enhanced strain to tensile failure by introducing fibre waviness

Unidirectional (UD) carbon fibre reinforced polymers offer high specific strength and stiffness but they fail in a catastrophic manner with little warning. Gas-texturing and non-constrained annealing were used to introduce fibre waviness into UD polyamide 12 composites produced by wet-impregnation hoping to produce composites with a more gradual failure mode and increased failure strain. Both methods increased the variation of fibre alignment angle compared to the control samples. The composites containing wavy fibres exhibited a stepwise, gradual failure mode under strain controlled uniaxial tension rather than a catastrophic failure, observed in control samples. Gas-texturing damaged the fibres resulting in a decrease of the tensile strength and strain to failure, which resulted in composites with lower tensile strength and ultimate failure strain than the control composites. Non-constrained annealing of carbon fibre/PA-12 produced wavy fibre composites with ultimate failure strain of 2%, significantly higher than 1.6% of the control composite.     

Failure strain as the key design criterion for fracture of natural fibre composites

Natural fibre composites are often considered to be problematic because of the high variability in their mechanical properties. This short communication considers the statistical variation in the two key fracture properties (strain and strength) for data obtained from tests on 785 jute technical fibres. The fibre strength does have high variability, which arises from the difficulty of determining an accurate fibre cross-sectional area (CSA). Failure strain is more consistent as this property is independent of the fibre cross-section. The authors therefore recommend that the use of failure strain as the key design criterion for natural fibre composites would expedite the adoption of these materials in the market.     

Damage in biocomposites: Stiffness evolution of aligned plant fibre composites during monotonic and cyclic fatigue loading

The non-linear stress–strain behaviour of plant fibre composites is well-known in the scientific community. Yet, the important consequences of this, in terms of the evolution of stiffness as a function of applied strain and cycles to failure, are not well-studied in literature. This is despite the fact that stiffness degradation is a well-accepted indicator of damage in a composite material, and is regularly used as a component failure criterion. This article systematically explores the evolution of stiffness of various aligned plant fibre composites, subjected to (i) monotonic loading, (ii) low-cycle, repeated progressive loading, and (iii) fatigue loading. The evolution in stiffness in plant fibre composites is found to be complex: structural changes in the elementary fibre cell wall and damage development in the composite have often competing effects on stress–strain behaviour. Indeed, the evolution in stiffness of plant fibre composites is found to be unlike that typically observed in traditional composites, and therefore needs to be taken into account in the design of structural components.     

Forming induced wrinkling of composite laminates: A numerical study on wrinkling mechanisms

When manufacturing composite aircraft components consisting of uni-directional prepreg laminates, Hot Drape Forming (HDF) is sometimes used. One issue with HDF is that, in contrast to hand lay-up where normally only one ply is laid up at a time, multiple plies are formed together. This limits the in-plane deformability of the stack, thus increasing the risk of out-of-plane wrinkling during forming. In this paper mechanisms responsible for creating different types of wrinkles are explained. It is shown through simulations how the wrinkles are created as a result of interaction between two layers with specific fibre directions or due to compression of the entire stack. The simulations are compared to experimental results with good agreement.     

Bending characterisation of a molten unidirectional carbon fibre reinforced thermoplastic composite using a Dynamic Mechanical Analysis system

The quality of forming simulations based on Finite Element methods is mainly determined by the accuracy of the material properties. Out-of-plane bending is one of the deformation mechanisms that govern the appearance of wrinkles while forming composite reinforcements. This paper proposes a new test method using a Dynamic Mechanical Analysis (DMA) system for the characterisation of longitudinal out-of-plane bending properties of molten unidirectional thermoplastics. Investigations are presented for a unidirectional carbon fibre reinforced polyamide 6 composite. Several standard bending test fixtures are assessed quasistatically at three temperatures and three test speeds with specimens of different geometries. Additional tests are conducted at forming temperature with the selected test arrangement. The evaluation of different approaches for the calculation of the bending modulus shows the interlaminar shear to be negligible. Results highlight an important material strain rate dependency. The evolution of the bending modulus satisfies a linear fitting within the range of data.     

Hybrid effects in thin ply carbon/glass unidirectional laminates: Accurate experimental determination and prediction

Experimental results are presented which allow the hybrid effect to be evaluated accurately for thin ply carbon/epoxy–glass/epoxy interlayer hybrid composites. It is shown that there is an enhancement in strain at failure of up to 20% for very thin plies, but no significant effect for thicker plies. Hybrid specimens with thick carbon plies can therefore be used to measure the reference carbon/epoxy failure strain. The latter is significantly higher than the strain from all-carbon specimens in which there is an effect due to stress concentrations at the load introduction. Models are presented which illustrate the mechanisms responsible for the hybrid effect due to the constraint on failure at both the fibre and ply level. These results give a good understanding of how variability in the carbon fibre strengths can translate into hybrid effects in composite laminates.     

Umformtechnologie: Prozesse – Werkstoff‐ charakterisierung – Simulation – Verifikation

Sheet forming technology – processes, materials, simulation and verification Hydroforming and Deep Drawing represent leading technologies for forming sheet metal components. The Materials Branch of the University of Duisburg‐Essen works since more than 10 years in the field of Hydroforming and showed that Hydroforming increases the strength and that the weldings of hydroformed tubes normally exhibit a same (fatigue) strength as the base material. For an improvement of the economics of hydroforming spliced tubes were considered and standard hollow nodes for tubes nodes structures were developed and a proposal was made to produce these tubes in variable tools with segments or lamellas. A significant increase in economics of Hydroforming and of Deep Drawing of components is achieved by an introduction of the principles of an integral (cooperative) development of products. At the University of Duisburg‐Essen the following stages are run through: CAD (the Material Branch uses PRO/ENGINEER®), forming simulation – for that PAM‐STAMP® (ESI) and PATRAN MARC MENTAT® (MSC) are used – FEM strength calculation and EVICD for a consideration of variable service loading. Forming simulation needs as basic material data the yield curve, the parameters of anisotropy and the Forming Limit Curve (FLC). For a determination of the FLC in Deep Drawing Tests suitable Nakazima specimens were developed by applying the principles of cooperative product development. The specimens could then successfully be validated in Deep Drawing Tests, which were instrumented by the advanced 3D‐forming‐analysis‐system AUTOGRID inProcess (VIALUX). Various other forming simulations were also performed and some general rules for the performance of forming simulations were formulated. Finally, reverse engineering is briefly discussed.     

复合材料累积破坏承载能力的预测

分析和总结了沿纤维方向单轴拉伸时复合材料的破坏机理,提出了一种复合材料应力－应变行为的预测方法,并通过树脂基复合材料的拉伸破坏试验,对此方法进行了验证。     

Modeling of localization and fracture phenomena in strain and stress space for sheet metal forming

In this study, a model based on a strain localization level to overcome the shortcomings of the well-established Forming Limit Diagram (FLD) in predicting the physical phenomenon of necking is introduced. An optical measurement system was used to capture the strain history of the Nakazima experiment until rupture occurred. In order to measure the fracture strain more accurately, a further method is introduced, which is based on the microscopic measurements of ruptured regions. This model is validated using a 3-point bending test. The results show the ability of the method to predict failure under bending conditions as well. Additionally, failure is investigated based on the pressure sensitivity and the Lode dependency. The results show that the triaxiality at the failure point is independent of the loading path.     

Local stress concentration and the prediction of tensile failure in unidirectional composites

The aim of this paper is to present a new representation of the tensile failure of a composite material which accounts for the normal stress supported by the matrix and allows a study of the influence of constituent material properties and fibre volume fraction on the stress-concentration factors. This is done by micromechanical analysis which allows the stress and strain in the fibres and the matrix to be related to the applied stress or strain on the composite. Stress-concentration factors are calculated in the composite transverse section and are found to be smaller than previously published analytical solutions. The difference is essentially due to the normal stress supported by the matrix which is neglected by the shear-lag analysis but is taken into account in our model. The tensile strength is calculated firstly by numerical simulations and secondly by Batdorf's methodology which addresses the formation and propagation of fibre fractures. Comparisons with experimental measures are satisfactory.     

The potential of harakeke fibre as reinforcement in polymer matrix composites including modelling of long harakeke fibre composite strength

Mechanical properties of aligned long harakeke fibre reinforced epoxy with different fibre contents were evaluated. Addition of fibre was found to enhance tensile properties of epoxy; tensile strength and Young’s modulus increased with increasing content of harakeke fibre up to 223 MPa at a fibre content of 55 wt% and 17 GPa at a fibre content of 63 wt%, respectively. The flexural strength and flexural modulus increased to a maximum of 223 MPa and 14 GPa, respectively, as the fibre content increased up to 49 wt% with no further increase with increased fibre content. The Rule of Mixtures based model for estimating tensile strength of aligned long fibre composites was also developed assuming composite failure occurred as a consequence of the fracture of the lowest failure strain fibres taking account porosity of composites. The model was shown to have good accuracy for predicting the strength of aligned long natural fibre composites.     

Influence of water ageing on mechanical properties and damage events of two reinforced composite materials: Flax–fibres and glass–fibres

Moisture absorption and durability in water environment are major concerns for natural fibres as reinforcement in composites. This paper presents a study on the influence of water ageing on mechanical properties and damage events of flax–fibre composites, compared with glass–fibre composites. The effects of the immersion treatment on the tensile characteristics, water absorption and acoustic emission (AE) recording were investigated. The water absorption results for the flax–fibre composites show that the evolution appears to be Fickian and the saturated weight gain is 12 times as high that the glass–fibre composites. Decreasing continuously with increasing water immersion time, the tensile modulus and the failure strain of flax–fibre composites are hardly affected by water ageing whereas only the tensile stress is reduced regarding the glass–fibre composites. AE indicate that matrix–fibres interface weakening is the main damage mechanism induced by water ageing for both composites.     

Local strain in a 5-harness satin weave composite under static tension: Part I - Experimental analysis

This paper presents an experimental method for determining the local strain distribution in the plies of a thermoplastic 5-harness satin weave composite under uni-axial static tensile load. In contrast to uni-directional composites, the yarn interlacing pattern in textile composites causes heterogeneous strain fields with large strain gradients around the yarn crimp regions. In addition, depending on the local constraints that are imposed by the surrounding plies, the deformation behavior of the laminate inner layers may vary from that of the surface layers, which are relatively more free to deform, compared to the inner layers. In order to validate the above hypothesis, the local strains on the composite surface were measured using digital image correlation technique (LIMESS). Internal strains in the composite laminate were measured using embedded fibre optic sensors (FOS).Based on the DIC results, the strain profiles at various locations on the composite surface were estimated. Using the FOS results, the maximum and minimum strain values in the laminate inner layers were evaluated. Comparison of the local strain values at different laminate positions provides an estimate of the influence of the adjacent layers on the local longitudinal strain behavior of a satin weave composite. Part II of this paper elucidates the local strain variation computed using the meso-FE simulations. In addition to the comparison of numerical and experimental strain profiles, Part II presents the maximum and minimum strain envelopes for the carbon-PolyPhenelyne Sulphide (PPS) thermoplastic 5-harness satin weave composite.     

Interfacial separation of fibres in fibre reinforced composites

An analytical model is proposed to predict the ultimate tensile strength of fibre-reinforced composites when the failure is governed by fibre debonding.

The analytical analysis is based on the principle of the compliance method in fracture mechanics with the presence of an interfacial crack at the fibre/matrix interface. The model is developed on the basis of the assumption that both the matrix and the fibre behave elastically and the matrix strain at a zone far from the matrix-fibre interface is equal to the composite strain. Furthermore, it is assumed that a complete bond exists between the fibre and the matrix and that the crack faces are traction free.

It is shown that the separation strain energy release rate for fibre-reinforced composites can be obtained for cases with and without the existence of an interfacial crack. Numerical examples are presented and compared with results obtained in the literature by finite element analyses and from experimental tests. The comparison demonstrates the accuracy and the convergence of the model.     

Matrix failure in composite laminates under compressive loading

The failure envelope of the matrix in composite laminates under compressive loads has not received much attention in literature. There are very little to no experimental results to show a suitable failure envelope for this constituent found in composites. With increasing popularity in the use of micromechanical analysis to predict progressive damage of composite structures which requires the use of individual failure criteria for the fibre and matrix, it is important that matrix behaviour under compression is modelled correctly.In this study, off-axis compression tests under uniaxial compression loading are used to promote matrix failure. Through the use of micromechanical analysis involving Representative Volume Elements, the authors were able to extract the principal stresses on the matrix at failure. The results indicated that hydrostatic stresses play an important role in the failure of the matrix. Thus, Drucker–Prager failure criterion is recommended when modelling compressive matrix failure in composite structures.     

Recycling of shredded composites from wind turbine blades in new thermoset polymer composites

As the energy produced from wind increases every year, a concern has raised on the recycling of wind turbine blades made of glass fibre composites. In this context, the present study aims to characterize and understand the mechanical properties of polyester resin composites reinforced with shredded composites (SC), and to assess the potential of such recycling solution. A special manufacturing setup was developed to produce composites with a controlled content of SC. Results show that the SC in the composites was well distributed and impregnated. The composite stiffness was well predicted using an analytical model, and fibre orientation parameters for strength modelling were established. The stress-strain curves revealed composite failure at unusual low strain values, and micrographs of the fracture surface indicated poor adhesion between SC and matrix. To tackle this problem, chemical treatment of SC or use of an alternative resin, to improve bonding should be investigated.