Simple model for consolidation of metal matrix coated SiC fibre composites

Abstract

A simple approach to modelling the consolidation of matrix coated fibre composites is presented. It employs an existing porous material constitutive model for monolithic materials. It is argued that in the consolidation of metal coated SiC fibres, the deformation primarily occurs in an outer layer of the fibre coating, and the internal core remains undeformed, largely because of the generally hydrostatic compressive loading, and because of the incompressible nature of the material in creep. The consolidation process is therefore not vastly different to that occurs for monolithic metal fibres, and similar equations can therefore be used for the composite consolidation. The constitutive equations have been implemented into general purpose non-linear finite element software within a large deformation formulation by means of two different user subroutines, one providing a general implementation, and the other a cpu time efficient approach. The manufacture and testing of SiC continuous fibre, Ti-6Al-4V metal matrix composite specimens is described and the results of the tests compared with the model calculations, showing that good agreement can be achieved with a simple model. The dependence of volume fraction of fibres and temperature can be introduced empirically through the specification of just two material constants. The model is therefore useful in the development of consolidation processes.     

复合材料蠕变本构关系及实验测定Ⅰ.本构关系

蠕变是复合材料最重要的力学性能之一,实验表明:复合材料在蠕变条件下的变形可以分为弹性变形、粘弹性变形和粘塑性变形.应用不可逆过程的热力学和广义变量的概念可以分析材料的蠕变变形.本文首先回顾了热力学的基本方程;基于Schapery本构关系的假设和思路推导了蠕变本构关系的一般形式,其中包括弹性变形、粘弹性变形和粘塑性变形;考虑到广义力选取的不唯一性,本文提出了广义力选取的原则以使得到的本构关系尽可能地简单;由此本文给出了复合材料的一维蠕变,各向同性复合材料的二维蠕变和纤维增强复合材料平面内的蠕变的本构关系.     

Governing equations for the steady state creep in orthotropic materials

Summary A general constitutive equation for creep deformation is presented based upon the concept of tensorial internal variables. The consequences of the theory of tensor functions representation are discussed with respect to the evolution equations. In a particular case of steady evolution of internal variables the governing equation for the secondary creep rate is derived in terms of a scalar inelastic potential. The material parameters required to characterize the stationary creep behaviour of the orthotropic composite are obtained from the unidirectional tension creep tests performed on a glass woven fabric xylok composite. Further check on the theory is made for the bidirectionally loaded specimens.With 4 Figures     

Experimental Study of the Creep Behaviour of the Cold‐Drawn 304L Stainless Steel

Abstract: In this article, the material and physical parameters for the creep constitutive equations of cold‐drawn 304L stainless steel have been determined using experimental data. Austenitic stainless steel 304L is used mostly in power generation and petrochemical industries because of its high‐temperature creep resistance even at above yield stresses. Test samples have been obtained from cold‐drawn bars, and the material conforms to ASTM A276‐05a specifications. The creep behaviour and properties have been examined for this material by conducting uni‐axial creep tests. Constant temperature and constant load uni‐axial creep tests have been carried out at three temperatures of 680,700 and 720 °C, subjected to constant loads which produce below and above yield initial stresses of 200, 250, 320, 340 and 360 MPa. The experimental data have been used to obtain the creep constitutive parameters using numerical optimisation techniques. In addition, the temperature and stress dependency of the creep properties for this alloy have been investigated using Larson–Miller and Monkman–Grant parameters.     

Experimental Study of the Creep Lifetime of the 1.25Cr 0.5Mo Steel Pipes

Abstract: In this paper, physical parameters for the creep constitutive equations of the low alloy ferritic steel 1.25Cr0.5Mo have been determined using experimental data. This alloy is used mostly in power generation and petrochemical industries because of its high temperature creep resistance. Test samples have been obtained from a new super‐heater pipe wall of a steam‐generating boiler in Tabriz Petrochemical Plant according to the ASTM standards. By conducting creep rupture tests for 1.25Cr0.5Mo steel, creep behaviour and creep‐rupture properties were examined for this material. Creep rupture tests have been carried out at four temperatures of 700, 725, 750 and 800 °C, under applied uni‐axial stresses of 30, 35, 40 and 50 MPa. The experimental data have been used to obtain the constitutive parameters using numerical optimisation techniques. Also the temperature and stress dependency of the creep lifetime for this alloy has been investigated using Larson–Miller and Monkman–Grant parameters. The results show good agreement with other test data such as ASTM and API. Finally, these constitutive equations have been used to study the creep behaviour of the super‐heater pipe. The results show that the super‐heater tube has been over designed in terms of the creep lifetime and this is in accordance with the in‐plant observations.     

复合材料蠕变本构关系及实验测定Ⅱ实验测定

在前一部分,本文得到复合材料蠕变的本构关系,在此基础上,本文进一步分析了复合材料蠕变本构关系的具体形式,实验测得了长纤维增强复合材料在蠕变、恢复两个阶段的应变,以用来确定本构关系中的待定参数,考虑到本构关系为复杂的非线性方程,本文提出了用离散变量和最小二乘法联合的方法确定参数,进而拟合蠕变本构关系的理论公式,分离出了蠕变过程中的弹性变形、粘弹性变形和粘塑性变形,对本构关系中的几个参函数,本文根据有限的实验数据拟合了其函数。      

复合材料蠕变本构关系及实验测定 Ⅱ实验测定

在前一部分,本文得到复合材料蠕变的本构关系,在此基础上,本文进一步分析了复合材料蠕变本构关系的具体形式,实验测得了长纤维增强复合材料在蠕变、恢复两个阶段的应变,以用来确定本构关系中的待定参数,考虑到本构关系为复杂的非线性方程,本文提出了用离散变量和最小二乘法联合的方法确定参数,进而拟合蠕变本构关系的理论公式,分离出了蠕变过程中的弹性变形、粘弹性变形和粘塑性变形,对本构关系中的几个参函数,本文根据有限的实验数据拟合了其函数.     

Physical basis for model with various inelastic mechanisms for nickel base superalloy

Abstract

Two mechanical behaviour models for N – 18 alloy are proposed. The material is a powder metallurgy nickel base superalloy hardened by 60% volume of the ordered γ′ phase. The behaviour of alloy N – 18 is modelled by classical constitutive equations involving plasticity and creep. The experimental data used include stress relaxation and creep tests. An updated version of the first model is proposed and compared to the experimental data set. A new model is also presented with equations based on physical concepts. Material parameter identification is performed for each model, and experimental results are in good agreement with theoretical simulations.     

Investigation of microstructure and mechanical properties of steel fibre–cast iron composites

Abstract

The aim of the present experimental study was to investigate improvement of the toughness and strength of grey cast iron by reinforcing with steel fibres. The carbon content of the steel fibres was chosen to be sufficiently low that graphite flakes behaving as cracks were removed by carbon diffusion from the cast iron to the steel fibres during the solidification and cooling stages. To produce a graphite free matrix, steel fibres with optimum carbon content were used and the reinforced composite structure was cast under controlled casting conditions and fibre orientation. Three point bend test specimens were manufactured from steel fibre reinforced and unreinforced flake graphite cast iron and then normalising heat treatments were applied to the specimens at temperatures of 800 and 850°C. The fracture toughness and strength properties of the steel fibre reinforced material were found to be much better than those of unreinforced cast iron. The microstructures of the composite at the fibre–matrix transition zone were examined.     

Development of a powder coated fibre pre-processing route for production of fibre reinforced composites

Abstract

As a critical material for next generation aeroengines, fibre reinforced composites such as silicon carbide reinforced titanium continue to attract strong attention from both industrial and academic sectors. Reducing the processing costs and increasing component processing flexibility remain the priorities of current research. This paper presents a novel powder coated fibre pre-processing technique to meet such industrial requirements. The proposed technique is based on slurry powder metallurgy and presents itself as a cost effective alternative to current processing methods. It involves firstly, mixing matrix powder particles with an appropriate organic binder and solvent to form a slurry, drawing a continuous silicon carbide fibre through the slurry, drying the coated fibre and finally laying up the fibres into a composite preform for subsequent consolidation. The organic component is removed from the preform matrix via a binder burnout phase prior to composite consolidation.     

Micromechanics of multiple cracking Part II Statistical tensile behaviour

A computational model for fibre-reinforced brittle materials in tension is developed. The model includes multiple cracking and strain-hardening processes, as well as single fracture and strain softening. The composite behaviour is derived from a single-fibre analysis by integrating over all possible fibre locations and orientations. The single-fibre analysis is based on symmetry fibres satisfying the equilibrium condition. The result is a complete constitutive relation: stress–strain or stress–crack width curve, and a prediction of crack spacing. The model is an extension of the ACK theory by Aveston, Cooper and Kelly, as it can be used with discontinuous fibres with different distributions, as well as for analysing hybrid composites. Fibre orientation introduces additional phenomena, which are taken into account with simple models. It was seen that matrix spalling at the fibre exit point may have a considerable effect on the composite strain and the crack width. The effect of fibre aspect ratio on the failure mode was studied, and it was found that with an intermediate fibre diameter the composite fails by fibre pull-out in a multiple-cracking stage, resulting in a strain-hardening material with a high ductility. The proposed model was verified against experimental results of a strain-hardening material, called an engineered cementitious composite. The model can be used in tailoring new materials to meet certain requirements, or in studying the effects of micromechanical properties on the composite behaviour, including the crack width, crack spacing, post-cracking strength, ultimate strain, and ductility. The derived constitutive relationship can further be used in finite element analyses defining the behaviour perpendicular to the crack. © 1998 Kluwer Academic Publishers     

Higher-order fractional constitutive equations of viscoelastic materials involving three different parameters and their relaxation and creep functions

Two higher-order fractional viscoelastic material models consisting of the fractional Voigt model (FVM) and the fractional Maxwell model (FMM) are considered. Their higher-order fractional constitutive equations are derived due to the models’ constructions. We call them the higher-order fractional constitutive equations because they contain three different fractional parameters and the maximum order of equations is more than one. The relaxation and creep functions of the higher-order fractional constitutive equations are obtained by Laplace transform method. As particular cases, the analytical solutions of standard (integer-order) quadratic constitutive equations are contained. The generalized Mittag–Leffler function and H-Fox function play an important role in the solutions of the higher-order fractional constitutive equations. Finally, experimental data of human cranial bone are used to fit with the models given by this paper. The fitting plots show that the models given in the paper are efficient in describing the property of viscoelastic materials.     

Finite element analysis of viscoelastic composite structures based on a micromechanical material model

The stress and creep analysis of structures made of micro-heterogeneous composite materials is treated as a two-scale problem, defined as a mechanical investigation on different length scales. Reinforced composites show by definition a heterogeneous texture on the microlevel, determined by the constitutive behaviour of the matrix material and the embedded fibres as well as the characteristics of the bonding properties in the interphase. All these heterogeneities are neglected by the finite element analysis of structural elements on the macroscale, since a ficticious and homogeneous continuum with averaged properties is assumed. Therefore, the constitutive equations of the substitute material should well reflect the mechanical behaviour of the existing micro-heterogeneous composite in an average sense.The paper at hand starts with the brief outline of a micromechanical model, named generalized method of cells (GMC), which provides the macrostress responses due to macrostrain processes as well as the homogenised constitutive tensor of the substitute material. The macroscopic stresses and strains are obtained as volume averages of the corresponding microfields within a representative volume element. The effective material tensor constitutes the mapping between the macro-strains and the macro-stresses. The cells method is used for the homogenisation of the unidirectionally reinforced single layers of laminates made of viscoelastic resins and flexibly embedded elastic fibres. The algorithm for the homogenisation of the constitutive properties runs simultaneously to the finite element analysis at each point of numerical integration and provides the macro-stresses and the homogenised constitutive properties. The validity of the proposed two-scale simulation is investigated by solving boundary value problems and comparing the numerical results for the structures to the experimental data of creep and relaxation tests or analytical solutions.     

Model for consolidation of Ti-6AI-4V/SiC fibre composite from plasma sprayed monotape

Abstract

A model has been developed for the consolidation of low pressure plasma sprayed (LPPS) titanium alloy matrix/silicon carbide fibre composites. Empirical constitutive equations were combined with an analytical model to describe the deformation of the rough surface region. The same constitutive equations were combined with alternately analytical and empirical yield criteria to describe the deformation of the regions of closed porosity surrounding the fibres. The two submodels were then combined with finite element analysis to make predictions of relative density and grain size as functions of pressure, temperature, and time, as well as predictions of the variations in porosity with position and fibre spacing. Experiments to validate the model were carried out using Archimedes' principle and both optical and scanning electron metallography. Data were found to agree reasonably well with predicted values.     

On diffusion creep of polycrystals

We present a variant of diffusion creep in polycrystalline bodies, which is based on solving a diffusion-viscous flow model problem. A polycrystal is treated as a composite material and the relevant boundary-value problem is solved through approximation of the self-consistent method. Simple expressions have been derived for viscosity coefficients of the polycrystal and grain boundaries. The creep equation is analyzed for a uniaxial compression case. The conclusions inferred from this equation are qualitatively consistent with the available experimental findings. Translated from Problemy Prochnosti, No. 3, pp. 14–24, May–June, 2009.     

A three-stage constitutive model for the creep behaviours of high-Cr steels at elevated temperatures

In this paper, a three-dimensional constitutive model is proposed to simulate the creep behaviours of high-Cr steels at elevated temperatures. In the model, the minimum creep rate and the average creep rupture time at different temperatures and stress levels are predicted by adopting two Larson–Miller parameters. The decrease of the creep rate during the primary creep stage is captured by introducing an internal variable representing the strain hardening effect. The material parameters of the model can be identified by using the conventional experimental results. Both the strain- and stress-driven algorithms are designed to solve the constitutive evolution equations. The response of high-Cr steels during the whole creep procedure can be predicted at a quantitative level by the current model. Further implementing the model into a finite element software, the global creep behaviours of high-Cr components under realistic loading conditions can be simulated.     

Determination of creep parameters from indentation creep experiments: a parametric finite element study for single phase materials

Abstract

This paper explores the possibilities of determining creep parameters for a simple Norton law material from indentation creep testing. Using creep finite element analysis the creep indentation test technique is analysed in terms of indentation rates at constant loads. Emphasis is placed on the evolving stress distribution in front of the indenter during indentation creep. Moreover the role of indenter geometry, size effects and of macroscopic constraints is explicitly considered. A simple procedure is proposed to translate indentation creep results into constitutive creep equations for cases where the dimensions of the tested material are significantly larger than the indenter. The influence of macroscopic constraints becomes important when the size of the indenter is of the same order of magnitude as the size of the testing material. As a striking example for size effects and for macroscopic constraints the indentation creep process in a thin film is analyzed. The results contribute to a better mechanical understanding of indentation creep testing.     

Constitutive modelling and springback prediction for creep age forming of 2124 aluminium alloy

Abstract

In order to improve the mechanical properties and reduce fabrication cost of large sheet metal parts, creep age forming (CAF) technology was developed, which is a process combined creep forming and heat treatment together. Springback of the workpiece in CAF is directly related to process parameters, such as, aging time, experimental stress and temperature. The aim of this paper is to establish a set of creep constitutive model, which can accurately predict the springback of 2124 aluminium alloy in CAF. A series of creep tests were carried out under different stress levels as 200, 225 and 250 MPa, and different temperatures as 185, 190 and 195°C for the solid solution treated and quenched 2124 aluminium alloy. Based on creep test data, a set of classic creep constitutive equations were established. Some important conclusions were drawn: the fitting curves of the constitutive equations could describe the test data in a good way; the creep strain increases with the increasing aging time, temperature and experimental stress. Then the springback of 2124 aluminium alloy during CAF process were analyzed by the finite element software MSC.Marc. Comparisons between the experiment analyses and finite element models show good correlation, and approve the forecast capability of FEM simulation for springback after CAF. At the end, the influence of process parameters on springback is studied, which provides essential foundation for designer to evaluate scheme and to optimise tool system design.     

Deterministic method for predicting the strength distribution of a fibre bundle

Owing to the non-strain hardening plastic behaviour of the aluminium matrix and the weak fibre/matrix interface, it has been shown that the strength of a carbon fibre-reinforced aluminium matrix composite made by diffusion bonding of prepreg layers can be derived from the corresponding fibre bundle strength. Application of Coleman's model to predict bundle strength leads to the conclusion that the composite must break when 15% of the fibres are broken. This greatly overestimates the experimental composite strength. Overestimations made by using the Coleman model are due to some implicit assumptions which are not valid in the case under consideration and which may consequently not describe our material. A new approach is proposed for the calculation of the strength distribution of a fibre bundle, based on the same fracture mechanism (fibres fracture progressively until the catastrophic fracture) but without restrictive assumptions. The real interpolated experimental fibre strength distribution (and not the Weibull distribution) is taken into account to predict bundle strength. The proposed method clearly shows the limit of strength prediction, in term of bundle size (number of fibres and gauge length). The risk of making predictions following the Weibull distribution out of the range of the observations (through single-fibre tensile tests) is demonstrated.     

The in-plane shear modulus of fibre reinforced composites as defined by the concept of interphase

In this paper we describe a model to find the approximate equations for determining the in-plane shear modulus of a unidirectional fibre reinforced composite from the constituent material properties. Classical elasticity theory has been applied to the simplified model of a composite unit cell in which the concept of an interphase between fibre and matrix is taken into account. Thus the model considers that the composite material consists of three phases, that is the fibre, the matrix, and the interphase which is the part of the polymer matrix lying close to the fibre surface which possesses different physico-chemical properties from those of the main constituents. Thermal analysis was used for the determination of the thickness and volume fraction of the interphase. The theoretical results are compared with other theoretical expressions and with experimental data. The model introduced in this paper seems to be an improvement for the shear modulus.