18 TH INTERNATIONAL CONFERENCE ON COMPOSITE MATERIALS MICROMECHANICAL MODELLING OF TEST SPECIMENS FOR ONSET OF DILATATIONAL DAMAGE OF POLYMER MATRIX IN COMPOSITE MATERIALS T. D. Tran 1 , D. Kelly 1* , G. Prusty 1 , G. Pearce 1 1 School of Mechanical and Manufacturing Engineering, University of New South Wales, Australia. *Corresponding author: d.kelly@unsw.edu.au Keywords : Finite-element analysis; Multiscale modelling; Onset theory; Dilatational strain invariant. 1 Introduction concentrations, especially for the cases where the fiber angle is 10 0 [3]. Furthermore, using the Recently, Gosse and Christensen [1] and Hart- Smith [2] have proposed a micromechanics failure continuum models to obtain the critical values theory for composites, called Strain Invariant requires strain enhancement factors to determine Failure Theory (SIFT), or more recently the Onset strains in the resin and fibers which takes time and Theory [3]. The onset theory is considered to be effort. To overcome these issues a new rigorous and have unique advantages over micromechanics modeling approach has been proposed. Application to modeling of the 10 0 off- traditional failure theories in that it is suitable for all possible laminate lay-ups, geometric axis specimen will be published elsewhere [5]. In this paper, the focus will be the 90 0 specimen configurations, loading and boundary conditions. To implement the theory, macroscopic strains including testing and micromechanical modeling. 2 The Damage Onset Theory determined by structural finite element analyses are enhanced by micromechanical strain In the approach proposed by Pipes and Gosse [3] amplification factors to determine representative strains from a continuum model of the laminate strains at the microscopic level. Damage onset is are enhanced by micro-mechanical strain predicted by comparing the micromechanical amplification factors to determine strains in the strain state to a set of critical strain invariants. resin including thermal residual strains from the In this paper, only matrix damage onset is cure. These amplification factors are determined considered. Damage onset within the fiber phase from unit cell finite element models, such as those is addressed elsewhere [4]. Gosse et al [1,3] have drawn in Fig. 1, that assume an arrangement of proposed that the polymer matrix fails either by fiber and resin. The square and hexagonal yielding or by cavitation. Matrix cavitation is arrangements shown in Figure 1 have been shown related to dilatational volume increase while to give bounding magnification factors and are yielding is related to dilatation free distortion. assumed to exist somewhere in the random Therefore, failure initiation in the matrix phase is distribution of fibers in the laminate. predicted by comparing the first dilatational strain invariant or a modification of the second distortional strain invariant to critical values determined from coupon tests. An important step in the theory is the establishment of the critical values of the strain invariants as material properties for the matrix. Work reported in [3] proposed off-axis Fig.1 . Square and hexagonal array representative unidirectional tests to generate these critical volume elements [6]. values. A 10 0 specimen gives the critical invariant for distortional behavior, while a 90 0 specimen The correct volume fraction for fiber and resin is gives the critical invariant for dilatational preserved in the unit cell models. Strains deformation. Finite element models of the test determined for the laminate in a finite element specimens are used to model the specimen at analysis are first scaled by the magnification failure and back out the critical values as values factors before the strain invariants are calculated using strains enhanced by the magnification and compared to the critical values to predict factors. failure. Modeling the response of the off-axis tensile tests is however challenging due to stress
ε critical Mathematically, the relationship between the = critical value distortional deformation. dis micro-strains and the macro-strains of a uni- Damage onset within the fiber phase is not directional composite laminate is given as [3,6]: addressed in this paper. � − � � � ∆� = � �� � ��̅ � ∆� (1) � � � − � � � ∆�� + � � Equation (1) emphasizes that intralaminar residual (�, � = 1 − 6) thermal effects are taken into account at the where: micromechanical level as well as at the laminate �̅ � − � � � ∆� = macro-strains due to mechanical and ε critical (or interlaminar) level. As long as and dil thermal loads ε critical � − � � for the polymeric matrix are known, the � ∆� =micro-strains at the k th point in the � � dis assessment of damage onset for the polymeric representative volume element (RVE) � =strain enhancement matrix at the k th point in matrix of composite structures can be performed. � �� Damage and crack propagation are actually a the Representative Volume Element (RVE) in Fig. repeated damage initiation phenomenon and 1 therefore a credible simulation of these damage � =thermal strain vector due to CTE mismatch of � � crack phenomena must be driven by the critical fiber and resin material properties of the constituent materials. ∆� =temperature drop from curing temperature to All effective interfacial phenomena are assumed operating temperature to be subsumed within the bulk response from the � � � = effective coefficient of thermal expansion of test. the laminate 3 Experiment for critical strain invariants for � = coefficient of thermal expansion of fiber or � � the matrix matrix depending on the k th point in the RVE. The onset theory states that if either the To determine the critical values of the strain dilatational strain invariant or the distortional invariants for the matrix, it would make sense to strain invariant exceeds their respective critical conduct experiments directly on the polymer values, damage initiation occurs [3, 6]. matrix of the composite. However, the The reduced form of the dilatational strain deformation of the polymer matrix in real invariant is as follows: unidirectional laminates is constrained by the ε = ε + ε + ε (2) fibers. To achieve this constrained strain state in a dil 1 2 3 neat resin test is a non-trivial problem which is and the distortional strain invariant is defined by: [ ] still under investigation. Currently the most 1 ( ) ( ) ( ) ε = ε − ε + ε − ε + ε − ε 2 2 2 practical way of determining the critical invariants (3) dis 1 2 1 3 2 3 6 for the matrix phase is via unidirectional where: composite tensile tests and then finite element ε =dilatational strain invariant analysis of these tests. The latest approach dil ε reported in [3] proposed a set of different off-axis =distortional strain invariant dis unidirectional tests from 10 0 to 90 0 to generate ε = principal strains. critical values of strain invariants for the matrix. A i 0 0 specimen will fail in the fibers and therefore is The detailed procedure for the micromechanical enhancement, including boundary conditions not included in this set for matrix failures. The applied to the RVE, is discussed in [6]. reason for choosing this set of tests is that the With the aid of micromechanical enhancement, a onset and ultimate failure typically occur detailed assessment of irreversible deformation is simultaneously in the off-axis tensile test in possible beyond the homogenous deformation contrast to the general case for ultimate behaviour state [3,6]: wherein damage propagation must occur before Damage onset within the matrix phase is onset can be detected. Consequently, the off-axis identified as: tensile test provides an excellent platform for ε ≥ ε critical evaluation of the damage onset for the polymer If , the matrix will cavitate. dil dil ε ≥ ε critical matrix. If dis dis , the resin will yield. Here ε critical = the critical value for dilatation dil deformation
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