Failure Mode Concept Research Articles

Omni first-ply-failure envelopes — A conservative approach to assess laminate failure

Omni first-ply-failure (FPF) envelopes are an elegant yet conservative approach to assess composite laminate failure on a global level. Omni envelopes can be found increasingly in recent publications. However, the development process of those envelopes shows a lack of clarity. At some point the illustration switches from a laminate-strain basis (ɛx,ɛy,γxy) to the particular case of laminate principal-strain (ɛI,ɛII) basis. The latter is elegant, as the principal-strain space can be easily plotted in 2D. This article presents two procedures to directly determine omni FPF envelopes and it clarifies the transfer to principal strains.While the Tsai–Wu criterion is used in almost all available publications, the present article uses Cuntze’s failure mode concept (FMC). The article provides a simple example case, which demonstrates the application of omni envelopes in context of FEA based CFRP design.

Distortional‐dilatational strain failure mode concept for hyperelastic materials

This work presents a universal, generally applicable, phenomenological failure criterion that describes a single, smooth, and convex hypersurface in principal strain space. It provides a strain‐based description of the bulk material failure of nearly incompressible hyperelastic elastomers and captures both distortional and volumetric failure in a single criterion.

An evaluation of Cuntze and Puck inter fibre failure criteria in simulation of thin CFRP plates subjected to low velocity impact

This paper presents the implementation and evaluation of a continuum damage mechanics-based material model to predict the damage and mechanical response of carbon fibre reinforced polymer composites subjected to low velocity impact. Failure mode concept model of Cuntze and Action plane strength model of Puck are employed as inter-fibre failure criteria in combination with non-linear shear behaviour and damage evolution using a user-defined material model in Abaqus/Explicit to account for the progressive damage in laminated composites. A novel approach has been used for the search of the fracture angle of Puck’s failure model to decrease the computational time of explicit simulations. Meanwhile, the simpler and less recognized failure model of Cuntze was implemented to simulate the low velocity impact on composites. The capability of the numerical model was established through a set of benchmark simulations on representative volume elements, tensile specimens, and low velocity impact cases. Both failure criteria were able to predict approximately the same shape and area for the matrix damage caused by the low velocity impact. Showing that the failure model of Cuntze is preferable to Puck since it does not require a search algorithm for the fracture angle and is more efficient for explicit simulations.

Determining the Damage and Failure Behaviour of Textile Reinforced Composites under Combined In-Plane and Out-of-Plane Loading.

The absence of sufficient knowledge of the heterogeneous damage behaviour of textile reinforced composites, especially under combined in-plane and out-of-plane loadings, requires the development of multi-scale experimental and numerical methods. In the scope of this paper, three different types of plain weave fabrics with increasing areal weight were considered to characterise the influence of ondulation and nesting effects on the damage behaviour. Therefore an advanced new biaxial testing method has been elaborated to experimentally determine the fracture resistance at the combined biaxial loads. Methods in image processing of the acquired in-situ CT data and micrographs have been utilised to obtain profound knowledge of the textile geometry and the distribution of the fibre volume content of each type. Combining the derived data of the idealised geometry with a numerical multi-scale approach was sufficient to determine the fracture resistances of predefined uniaxial and biaxial load paths. Thereby, Cuntze’s three-dimensional failure mode concept was incorporated to predict damage and failure. The embedded element method was used to obtain a structured mesh of the complex textile geometries. The usage of statistical and visualisation methods contributed to a profound comprehension of the ondulation and nesting effects.

Coupled distortional-dilatational failure mode concept for silicone adhesives

Nearly incompressible rubber-like materials, such as silicone adhesives, exhibit two failure modes: dilatational and distortional failure. The former corresponds to the formation and growth of cavities owing to triaxial deformation. The latter corresponds to fracture due to excessive isochoric deformation, i.e. deformation at constant volume. Both failure modes are typically assessed individually and corresponding failure criteria are often formulated in terms of stresses. However, stress-based descriptions of failure depend explicitly on the choice of constitutive law and the experimental measurement of critical stresses is challenging or even impossible. Therefore, recent studies proposed strain and stretch-based criteria for distortional failure of nearly incompressible hyperelastic materials, that can be obtained directly from optical measurements using digital image correlation.The present work exploits stretch-based descriptions of both failure modes to provide a unified coupled dilatational-distortional failure criterion which describes the complete failure surface of nearly incompressible silicone adhesives or rubber-like materials in general. For this purpose, we propose a stretch-based cavitation criterion which depends on a single parameter. Distortional failure is described by the Podgórski-criterion formulated in principal stretch space. The coupled dilatational-distortional failure criterion is validated using uniaxial tension, bulge and pancake tests of the nearly incompressible hyperelastic transparent structural silicone sealant DOWSIL™ TSSA. It is shown that the proposed failure criterion captures both the onset of cavitation and ultimate distortional failure in very good agreement with all experiments.

Determination of stresses, strains and failure types in multidirectional laminates under pure bending

Curved structures made of fibre-reinforced plastics tend to show an out-of-plane failure type, when loaded under bending. One method to determine the related tensile strength in thickness direction, is the standardised unfolding test related to ASTM D6415 with L-profile specimens. However, the standard shall be used for unidirectional materials only, which is not the case for multidirectional laminates. Therefore, this publication presents methods to determine the layer-wise stress and strain state as well as occurring failure types of multidirectional laminates. An extension of the Lekhnitski formulae is presented and its results are validated by comparison with high resolution strain measurements by Digital Image Correlation. Based on the analytical solution, a failure analysis using Cuntze’s Failure Mode Concept is conducted. It was revealed, that the failure load and position can be predicted accurately, if a failure type related strength –in-plane or out-of-plane failure– is used. In the presence of [Formula: see text]-layers higher deviations occur between test and prediction and therefore limits the validity of the presented analytical failure analysis.

A pragmatic approach for a 3D material model considering elasto-plastic behaviour, damage initiation by Puck or Cuntze and progressive failure of fibre-reinforced plastics

Fibre reinforced plastics with tough epoxy and thermoplastic matrices are spreading increasingly in many lightweight applications. For an efficient and reliable design the mechanical behaviour, considering non-linear plasticity, various failure modes under complex loading and damage progression, has to be estimated with numerical simulations. Most state-of-the-art continuum damage mechanics models do not consider the non-linear behaviour of the matrix material or are not suited for 3D solid elements. This work proposes a combined 3D continuum damage/plasticity model. It uses a single parameter flow criterion in combination with Cuntze’s Failure Mode Concept (FMC) for intralaminar failure. The FMC requires no iterative fracture angle search as the Action Plane Strength Criterion by Puck (APSC). This work describes details of the developed model like the coupling of the FMC with a degradation model as well as the implementation into Abaqus/Standard. A validation against open-hole tension tests made out of AS4/PEEK from literature is performed. It can be shown that the prediction of experimental failure loads with the FMC as well as with the APSC provides comparable results. The maximum deviations are between -7.85% and +12.85%. However, the computation times for predictions with the FMC are significantly less than with the APSC.

Experimental and numerical investigation of the transition zone of locally steel-reinforced joining areas under combined tension–bending loading

In modern lightweight structures, the use of fasteners is preferred to other joining techniques. An approach to increase the bearing strength is the local metal hybridisation, where carbon fibre-reinforced plastics layers are substituted locally by metal foils of the same thickness. The local replacement leads to a transition zone between the hybrid region and the pure carbon fibre-reinforced plastics region. The present work deals with the investigation of different transition zone patterns of carbon fibre-reinforced plastics-steel hybrid specimens in combined tension–bending tests and accompanying non-linear static simulation. The simulation includes delamination and intralaminar damage with the use of a cohesive zone model and Cuntze’s failure mode concept. Furthermore, residual thermal stresses are considered. A satisfying agreement of test and simulation is achieved, which allows the identification of beneficial transition zone configurations and also validates the numerical model for further parametric studies.

A three‐dimensional progressive damage model for fiber reinforced composites with an implicit‐explicit integration scheme

AbstractThis contribution proposes a fully three dimensional “continuum damage model” (CDM) to describe the interlaminar and intralaminar failure mechanisms of transversely isotropic elastic‐brittle materials under static loading. The constitutive model is derived from an energy function with independent damage variables for each damage mode. The evolution law is based on energy dissipation within the damage process, taking into account the critical energy release rate to weaken the effect of mesh dependent outcome. The onset of damage can be predicted with Cuntze's failure mode concept [1] as well as with Hashin's failure criteria. In this model linear stress decreasing is assumed. In addition, an implicit‐explicit integration scheme, first proposed by Oliver [3] for isotropic damage models, is adapted to increase the stability and robustness of numerical simulations and to decrease the computational cost of material failure analyses. By comparing the results from implicit‐explicit integration schemes and standard implicit integration schemes, a high level of agreement is found. (© 2015 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)

Experimental Study of the Seismic Behavior of an Earthquake-Damaged Reinforced Concrete Frame Structure Retrofitted with Basalt Fiber-Reinforced Polymer

A one-bay two-story reinforced concrete (RC) frame structure with weak beam-column joints was damaged during structural vibration control testing using a shake table. A damage assessment of the structure was conducted, and the structure was repaired using epoxy injection and retrofitted using basalt fiber-reinforced polymer (BFRP) sheets and retested. A seismic retrofit design method using fiber-reinforced polymer (FRP) for low-rise frame structures was proposed on the basis of mechanical analysis of the FRP-retrofitted structural components and the failure mode concept. The effective stiffness of each story increased notably after epoxy injection and FRP retrofitting. The shake table tests of the FRP-retrofitted structure showed that the shear capacity, ductility, and hysteretic energy dissipation capacity of each story were greatly improved and that the beam-column joint failure mode was prevented and the structure experienced much less damage compared with the original structure when subjected to ground motions of the same intensity. No debonding between the FRP sheets and the joints was observed after the shake table tests.

The predictive capability of failure mode concept-based strength conditions for laminates composed of unidirectional laminae under static triaxial stress states

This paper represents the author’s contribution to the second world-wide failure exercise using his failure mode concept modelling capability. The second world-wide failure exercise deals with the behaviour of isotropic material and unidirectional as well as multidirectional unidirectional laminae-composed laminates subjected to three-dimensional (triaxial) states of stress. Twelve challenging test cases were provided by the organisers and those covered stress–strain curves and failure envelopes under three-dimensional stress states. The application of the new failure mode concept model has extended the three-dimensional modelling by taking into account the effects of hydrostatic pressure and second glass temperature shift factor on the stress–strain curves and failure envelopes. The failure mode concept model was capable of successfully solving the majority of all the problems and a comparison between the predictions and test data is planned to be published in Part B of the second world-wide failure exercise.

Comparison between experimental and theoretical results using Cuntze’s “failure mode concept” model for composites under triaxial loadings—Part B of the second world-wide failure exercise

This paper represents a comparison between the predictions of Cuntze’s Failure Theory, referred to as ‘failure mode concept model, and experimental results provided in Part B of the second World-Wide Failure Exercise. The results covered 12 test cases, involving an isotropic matrix material, 7 UD laminas and 4 multi-directional laminates subjected to 3D states of stress. The UD lamina data, needed for the validation of the failure mode concept-based UD strength conditions, were broadly applicable, whereas the laminate data could only partly serve for model verification because some test cases show some discrepancies. Also, there was a lack of test data in some of the test cases and it is concluded that there is a need to obtain more representative test data. Nevertheless, a good mapping could be achieved by the applied strength conditions dedicated to the specific test case.

A phenomenologically based damage model for 2D and 3D-textile composites with non-crimp reinforcement

The application of textile-reinforced composites for safety-relevant structural components requires reliable predictions about their damage and failure behaviour. The potential of these materials for engineering applications has not been fully exploited so far since practical design rules disallow the occurence of any damage in the material even if the damage is not critical. In this context, the paper presents a novel damage model for textile composites with quasi-unidirectional reinforcement. A failure criterion based on the failure mode concept is adopted to describe the quasi-brittle fracture behaviour. To take into account the subsequent non-linear stiffness degradation, this approach is combined with a continuum damage mechanics model. The capability of the damage model is shown for biaxially reinforced weft-knitted glass fibre–epoxy composites.

Efficient 3D and 2D failure conditions for UD laminae and their application within the verification of the laminate design

Abstract The paper presents a set of three-dimensional (3D) and 2D strength failure conditions for unidirectional (UD) laminae made from fibre-reinforced plastics (FRP). The conditions are based on a concept termed the failure mode concept (FMC) which provides failure conditions formulated on UD lamina level that allows for a prediction of the critical lamina failure mode, and finally of laminate failure. Following the FMC there are five independent conditions: for inter fibre failure (IFF) three and for fibre failure (FF) two conditions. These are based on averaged lamina stresses. The IFF conditions were basically developed in 1996 and later contributed [Cuntze RG, Freund A. The predictive capability of failure mode concept-based strength criteria for multidirectional laminates. Part A. Compos Sci Technol 2004;64:343–77; Cuntze RG. The predictive capability of failure mode concept-based strength criteria for multidirectional laminates. Part B. Compos Sci Technol 2004;63:487–516] to a ‘World-Wide Failure Exercise (WWFE) on failure theories’ [Hinton MJ, Soden PD. Predicting failure in composite laminates: the background to the exercise. Compos Sci Technol 1998;58(7):1001–10]. In this paper a single but effective modification of one IFF condition is highlighted. It consists in the replacement of the ‘shear mode IFF 2’ by a numerically advantageous simplified formulation for the 3D and for the 2D case. A very satisfying verification of the 3D IFF2 condition, reduced to 2D, as well as for a directly formulated 2D IFF2 condition has been achieved when judging them versus the 2D experiments provided by the WWFE and other sources. As design verification demands for an accurate determination of the reserve factor. Its determination is presented for both the linear and the non-linear case. Values are given for one example.

The predictive capability of failure mode concept-based strength criteria for multidirectional laminates

This contribution is a post-runner to the ‘failure exercise’. It focuses on two aspects of the theoretical prediction of failure in composites [1–3]: the first is the derivation of failure conditions for a unidirectional (UD) lamina with the prediction of initial failure of the embedded lamina, and the second the treatment of non-linear, progressive failure of 3-dimensionally stressed laminates until final failure. The failure conditions are based on the so-called Failure Mode Concept (FMC) which takes into account the material-symmetries (by the application of invariants) of the UD-lamina homogenized to a ‘material’, and on a strict failure mode thinking. The results of the investigation are stress–strain curves for the various given GFRP-/CFRP-UD-laminae, biaxial failure stress envelopes for the UD-laminae, and initial as well as final biaxial failure envelopes for the laminates. In addition a brief comparison between Puck's and Cuntze's failure theory is presented by the authors themselves.

The predictive capability of failure mode concept-based strength criteria for multi-directional laminates—part B

This paper represents the author's contribution to Part B of the worldwide failure exercise. An assessment is made of the correlation between the predictions, published in Part A, and experimental results provided for 14 test cases involving bi-axial initial and final failure envelopes and stress strain curves of various unidirectional and multidirectional laminates. The theory, implemented into a computer code, employs 3D failure criteria for UD laminae together with non-linear modelling of laminae and laminate. The criteria are based on the author's Failure Mode Concept (FMC). Some simplifications of the failure criteria have been made and an improvement in the computer code so that large strains to failure may be captured. Special emphasis has been put on the difference between an isolated and an embedded UD lamina. The correlation between the predictions and the test data is very satisfactory for the UD laminae, and is generally satisfactory for the laminates, especially where Fibre Failure (FF) is the dominant mode, which is the case for well-designed (according to netting theory) laminates. Discrepancy between predictions and test data was largest for the±55° angleply glass/epoxy laminates and also in areas of large deformations (involving post failure progression beyond the occurrence of the various Inter Fibre Failure (IFF) modes). Further steps, including testing and modelling, are identified for achieving a better understanding of failure prediction.

The failure mode concept in reliability engineering : C. Boe. Proc. 1974 Reliability and Maintainability Symposium, U.S.A. 281 (29–31 Jan. 1974)

The failure mode concept in reliability engineering : C. Boe. Proc. 1974 Reliability and Maintainability Symposium, U.S.A. 281 (29–31 Jan. 1974)