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Journal ArticleDOI

Measurement of resistance curves in the longitudinal failure of composites using digital image correlation

TL;DR: In this paper, the authors presented a new methodology to measure the crack resistance curves associated with fiberdominated failure modes in polymer-matrix composites, which is based on the identification of the crack tip location using Digital Image Correlation and the calculation of the J-integral directly from the test data using a simple expression derived for cross-ply composite laminates.
About: This article is published in Composites Science and Technology.The article was published on 2010-11-15 and is currently open access. It has received 175 citations till now. The article focuses on the topics: Digital image correlation & Composite laminates.

Summary (2 min read)

1. Introduction

  • Sophisticated kinematic representations of failure mechanisms [8,9], and cohesive elements to deal with delamination [10,11], the accurate prediction of intralaminar fracture mechanisms still presents several challenges.
  • While this assumption is valid under smallscale bridging conditions, the shape of the cohesive law plays a fundamental role in the prediction of fracture under large-scale bridging conditions [12].
  • To account for these different failure mechanisms, a combined linear-exponential softening law for fiber tensile fracture has been proposed [5,6], and it was demonstrated that a simple linear softening law is unable to predict the load–displacement relation obtained in a cross-ply Compact Tension (CT) test specimen, while a bi-linear softening law provides an accurate prediction [13].
  • In addition, the experimental determination of the exact location of the tip of a kink-band is even more difficult than for the CT specimens.
  • An automatic algorithm that post-processes the full-field data provided by the DIC system during the CT and CC tests is used to detect the crack tip location and to establish the R-curve from the surface measurements of the displacement and strain fields.

2. Identification of the crack tip location

  • The algorithm used to identify the crack tip location in the CT and CC test specimens is based on the work of Grégoire [19].
  • The contour integral J, which is defined along a region where the material is linear-elastic, is therefore used to calculate the crack resistance curve of the CC and CT test specimens.
  • The same happens with the sum of the thicknesses of the all the 90 plies.
  • To simplify the calculations, the simple rectangular contour shown in Fig. 6 is selected.
  • The differentials dx1 and dx2 are taken as the differences between the centers of adjoining subsets, measured along the corresponding axes.

4.1. Configuration of the test specimens

  • The material used in this work is unidirectional carbon-fiber reinforced epoxy Hexcel IM7-8552.
  • The elastic properties of IM7-8552, measured in a previous investigation [18], are shown in Table 1. E1 and E2 are the longitudinal and transverse.
  • The specimens were finally machined to their final geometry, shown in Fig. 7 (CT specimen), and in Fig. 8 (CC specimen).
  • In the set-up, the optical system was positioned perpendicular to the surface of the specimen mounted into the testing machine (Fig. 9).
  • The facet step (i.e., the distance between adjacent facets) can also be set either for controlling the total number of measuring points over the region of interest, or for enhancing the spatial resolution by slightly overlapping adjacent facets.

4.2. Compact tension

  • The load was measured using the 100 kN load cell, and the displacement was measured using the linear variable differential transformer (LVDT) connected to the hydraulic actuator of the test machine.
  • Fig. 12 shows a good correlation between the FEM and DIC data reduction methods.
  • This means that the fracture process zone that bridges the crack has a minor effect on the displacement and strain fields in the regions where the Finite Element model computes the J-integral.
  • Fig. 13 shows the R-curves obtained from the three CT tests.
  • Fig. 13 also shows the mean value of the fracture process zone, 3.4 mm, and the mean values of the initial fracture toughness and that corresponding to steady-state crack propagation, 97.8 kJ/m2 and 133.3 kJ/m2 respectively.

4.3. Compact compression

  • A non-linear response is observed in the load–displacement relation before the peak load is attained.
  • The reason for this fact is that the FEM-based calculation of the J-integral does not account for the contact and load transfer across the band of the kinked fibers.
  • On the other hand, the DIC-based method uses the actual displacement and strain fields on the surface of the specimen, provided that the contours selected do not include delaminated regions, thus resulting in an improved R-curve.
  • Delamination associated with the propagation of the kink-band from the initial notch was also observed in the CC tests.
  • In addition, the presence of delamination invalidates the assumption of a two-dimensional crack, and of constant strain through the thickness of the laminate (assumption used in Eq. (6)).

5. Conclusions

  • This paper presents a new method to measure the crack resistance curves in CT and CC test specimens manufactured using cross-ply CFRP composite laminates.
  • The method was implemented in a ”Matlab” code that obviates the need of any complex pre- and post-processing of the test data, either based on FEM or standard data reduction methods, and enables the real-time generation of R-curves during a test.
  • The mean value of the associated cohesive zone is 3.4 mm.
  • The DIC-based method is an improvement over FE-based data reduction methods because it is based on the actual displacement field on a pre-defined contour that does not include delaminated regions.
  • The values computed for the fracture toughness using the CC specimen do not account for the energy dissipated by the delamination that accompanied the propagation of the kink-band.

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Citations
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Journal ArticleDOI
TL;DR: In this article, an innovative fatigue model based on configurational force is proposed to predict the mixed-mode fatigue crack propagation in elastic-plastic material, which can provide the estimation of crack initiation, crack deflection, and residual fatigue lifetime simultaneously.

9 citations

Journal ArticleDOI
TL;DR: In this article, the authors performed a systematic experimental analysis of the translaminar fracture behavior of high performance biocomposites constituted by green epoxy reinforced by sisal fibers, by varying the main influence parameters as fiber concentration and lay-up.

9 citations

Journal ArticleDOI
TL;DR: In this paper , the authors performed a systematic experimental analysis of the translaminar fracture behavior of high performance biocomposites constituted by green epoxy reinforced by sisal fibers, by varying the main influence parameters as fiber concentration and lay-up.
Abstract: The present work performs a systematic experimental analysis of the translaminar fracture behavior of high performance biocomposites constituted by green epoxy reinforced by sisal fibers, by varying the main influence parameters as fiber concentration and lay-up. Despite the corrective function properly introduced to take into account the anisotropy as well as the use of the equivalent crack length, the study shows that the LEFM does not give accurate estimations of the fracture toughness, because the extension of the near tip damaged zone is higher than the singular dominated one. Accurate estimations can be obtained instead by the proposed modified area method that takes into account both the local damage and the fiber bridging that occurs during crack propagation, that lead to R -curves whose asymptotic values constitute the true fracture toughness of the biocomposites examined. The constancy of the damage mechanisms observed by varying the fiber concentration, allows the user to compute the fracture toughness of a generic laminate from the specific fracture energy of the unidirectional lamina. Finally, the relatively high fracture toughness of the examined laminates allows to state that they can advantageously replace not only other composites having lower toughness, but also metals as steel, aluminum and titanium.

9 citations

Journal ArticleDOI
TL;DR: In this paper , the translaminar fracture toughness of composites reinforced with three types of high-performance polymer fibres: polyarylate (PAR), polybenzobisoxazole (PBO), and aramid fibre was investigated.
Abstract: The translaminar fracture toughness is a key property that governs the damage tolerance and notch sensitivity of fibre-reinforced composites. Compact tension tests were performed to investigate the translaminar fracture toughness of composites reinforced with three types of high-performance polymer fibres: polyarylate (PAR), polybenzobisoxazole (PBO) and aramid fibre. A carbon fibre composite was used as the reference system. The propagation translaminar fracture toughnesses of the PAR and PBO fibre composites were 492 kJ/m2 and 547 kJ/m2, respectively. These are among the highest translaminar fracture toughness values recorded in the literature. It was hypothesized that the fibrillation of the fibres upon failure was an important energy dissipating mechanism alongside pull-outs that were much longer than for carbon fibre. Replacing a small strip of a carbon fibre ply by a strip of PAR or PBO fibres successfully reinforced the material by locally arresting crack growth. By contrast, the performance of the aramid fibre composites and their hybrids with carbon fibre was lacklustre. The results presented in this work can be used to further improve the safety of composite parts by optimising the design for damage tolerance while also reducing the weight of the parts.

8 citations

Journal ArticleDOI
TL;DR: In this paper, the failure of fibers inside the yarns of 3D woven carbon/epoxy composites is investigated experimentally by estimating the critical energy release rate G C, through the analysis of Compact Tension (CT) and Single Edge Notched Beam (SENB) specimens.

8 citations

References
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Journal ArticleDOI
James R. Rice1
TL;DR: In this paper, an integral is exhibited which has the same value for all paths surrounding a class of notches in two-dimensional deformation fields of linear or non-linear elastic materials.
Abstract: : An integral is exhibited which has the same value for all paths surrounding a class of notches in two-dimensional deformation fields of linear or non-linear elastic materials. The integral may be evaluated almost by inspection for a few notch configurations. Also, for materials of the elastic- plastic type (treated through a deformation rather than incremental formulation) , with a linear response to small stresses followed by non-linear yielding, the integral may be evaluated in terms of Irwin's stress intensity factor when yielding occurs on a scale small in comparison to notch size. On the other hand, the integral may be expressed in terms of the concentrated deformation field in the vicinity of the notch tip. This implies that some information on strain concentrations is obtainable without recourse to detailed non-linear analyses. Such an approach is exploited here. Applications are made to: Approximate estimates of strain concentrations at smooth ended notch tips in elastic and elastic-plastic materials, A general solution for crack tip separation in the Barenblatt-Dugdale crack model, leading to a proof of the identity of the Griffith theory and Barenblatt cohesive theory for elastic brittle fracture and to the inclusion of strain hardening behavior in the Dugdale model for plane stress yielding, and An approximate perfectly plastic plane strain analysis, based on the slip line theory, of contained plastic deformation at a crack tip and of crack blunting.

7,468 citations

Journal ArticleDOI
TL;DR: In this article, the authors proposed fracture analysis of structural members made of FRP composites and derived the fracture angle which is the key for this evaluation, which is derived in the present paper.

1,529 citations

Journal ArticleDOI
TL;DR: In this paper, a thermodynamically consistent damage model is proposed for the simulation of progressive delamination in composite materials under variable-mode ratio, and a constitutive equation is developed to model the initiation and propagation of delamination.

820 citations


"Measurement of resistance curves in..." refers background in this paper

  • ...Despite the significant advances in the analysis models for the prediction of fracture in composite materials such as advanced failure criteria and associated damage models [1–7], sophisticated kinematic representations of failure mechanisms [8,9], and cohesive elements to deal with delamination [10,11], the accurate prediction of intralaminar fracture mechanisms still presents several challenges....

    [...]

Journal ArticleDOI
TL;DR: In this article, an anisotropic damage model suitable for predicting failure and post-failure behavior in fiber-reinforced materials is presented, which is intended to predict behavior of elastic-brittle materials that show no significant plastic deformation before failure.
Abstract: This paper presents an anisotropic damage model suitable for predicting failure and post-failure behavior in fiber-reinforced materials. In the model the plane stress formulation is used and the response of the undamaged material is assumed to be linearly elastic. The model is intended to predict behavior of elastic-brittle materials that show no significant plastic deformation before failure. Four different failure modes – fiber tension, fiber compression, matrix tension, and matrix compression – are considered and modeled separately. The onset of damage is predicted using Hashin’s initiation criteria [Hashin Z, Rotem A. A fatigue failure criterion for fiber-reinforced materials. J Compos Mater 1973;7:448; Hashin Z. Failure criteria for unidirectional fiber composites. J Appl Mech 1980;47:329–34] and the progression of damage is controlled by a new damage evolution law, which is easy to implement in a finite element code. The evolution law is based on fracture energy dissipation during the damage process and the increase in damage is controlled by equivalent displacements. The issues related to numerical implementation, such as mesh sensitivity and convergence in the softening regime, are also addressed.

769 citations

Journal ArticleDOI
TL;DR: A continuum damage model for the prediction of the onset and evolution of intralaminar failure mechanisms and the collapse of structures manufactured in fiber-reinforced plastic laminates is proposed in this article.

686 citations


"Measurement of resistance curves in..." refers background in this paper

  • ...To account for these different failure mechanisms, a combined linear-exponential softening law for fiber tensile fracture has been proposed [5,6], and it was demonstrated that a simple linear softening law is unable to predict the load–displacement relation obtained in a cross-ply Compact Tension (CT) test specimen, while a bi-linear softening law provides an accurate prediction [13]....

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This paper presents a new methodology to measure the crack resistance curves associated with fiberdominated failure modes in polymer–matrix composites.