Jan Bäcklund

Tensile Fracture of Laminates with Holes

The methods currently used for predicting static fracture of notched composite laminates in tension, such as the point and average stress criteria and the inherent flaw criterion, are of semi-empirical nature and have limited applicability with respect to size and shape of the notch. In this paper, a damage zone analysis, based on more fundamental concepts, is used to predict fracture of laminates with circular holes of various radii, and oval and rectangular holes of various sizes. The damage is represented by a linear cohesive zone. Based on the two fundamental parameters unnotched tensile strength (σ0) and apparent fracture energy (G*c), this model excellently predicts the strength of notched laminates for a number of specimens tested.

Fracture analysis of notched composites

Abstract Static fracture of notched composites has drawn the attention of numerous researchers in recent years and it has been studied both experimentally and theoretically. One of the proposed theories for predicting fracture of composites is the “average stress criterion” due to Whitney and Nuismer. A similar theory based on fracture mechanics has been used by Waddoups et al . Pipes et al have recently generalized these concepts by introducing a three-parameter fracture model and a radius superposed method. In the present paper the mechanisms behind the cut-off of the stress peak at the notch are investigated using the fictitious crack model (FCM). In the intense energy region close to the notch, a fictitious crack is assumed to form when the uniaxial tensile strength is exceeded. On the surfaces of this fictitious crack, cohesive forces act. These forces reduce with increased width of the fictitious crack and vanish at a certain crack width. Hereafter the crack is considered as a real crack. The reduction of the cohesive forces can be assumed to follow various curves, three of which are shown in Fig. 1(b). A common feature for all curves is however, that the area under the curve is equal to the fracture energy ℷ c . It should also be emphasized that the fictitious crack merely represents a damaged zone in the composite than a sharp crack. Some preliminary finite element calculations performed with the fictitious crack model show good correlation with experimental results and the redistribution of stresses at increased external load is illustratively demonstrated.

Tensile Fracture of Laminates with Cracks

In this paper a method, called the Damage Zone Model (DZM), is used for predicting strength of composites with through-the-thickness cracks. The DZM is based on the two fundamental parameters unnotched tensile strength (σ0) and apparent fracture energy (G*c). The damage zone, developed at a notch in the composite, is modelled as a crack with cohesive forces acting on the crack surfaces. Redistribution of stresses and change in stiffness is accounted for in the model. For comparison, strengths are also calculated by semi-empirical methods such as the inherent flaw and the point stress criteria. Experimental results for three point bend (TPB), single edge notch (SEN) and compact tension (CT) quasi-isotropic carbon/epoxy specimens are presented. Some results for specimens made from randomly oriented short glass fiber/polyester specimens are also discussed. The damage zone model is shown to accurately predict fracture load, load- deformation behaviour and damage zone sizes in these types of laminates.

PVC sandwich core materials: Mode I fracture toughness

Abstract The fracture of a cracked PVC sandwich core material has been investigated. Mode I fracture toughness is evaluated using linear elastic fracture mechanics (LEFM), nonlinear fracture mechanics and a damage zone model. For the crack sizes and structural dimensions relevant to sandwich constructions, LEFM is not applicable according to the ASTM standard requirements for metals. However, the results show that the deviation between nonlinear analyses and LEFM is relatively small. Therefore, K Ic and G Ic can still be used for engineering purposes. It is also found that the fracture toughness depends on the average cell size.

Notch sensitivity of thermoset and thermoplastic laminates loaded in tension

Inplane tensile fracture of unnotched and notched thermoset graphite-epoxy and thermoplastic graphite-PEEK composite laminates is examined. Both fibre-dominated quasi-isotropic and matrix dominated ±45 angle-ply layups were investigated.Classical lamination theory predictions of elastic and strength properties of unnotched specimens are compared with experiments. Several notched geometries, i.e. centre-notched, double-edge notched and open-hole specimens subjected to tensile loading to fracture were examined. The notched strength of the quasi-isotropic laminates was analysed by a damage zone model, where damage around the notch is represented by an “equivalent crack” with cohesive force acting between the crack surfaces.Good agreement between experimental and calculated strength was observed for the graphite-epoxy laminates which failed in a collinear manner. For the graphite-PEEK laminates discrepancies between predicted and experimental strength are related to observed deviations from collinear crack growth. The angle-ply graphite-PEEK laminates showed larger notch sensitivity than the corresponding graphite-epoxy, probably due to less degree of stress relieving damage formation around the notch.

On design of joints between composite profiles for bridge deck applications

Techniques for joining of pultruded composite profiles for bridge-deck applications are designed and analyzed. It is shown that both adhesively bonded and bolted joints can be designed to fulfill stringent requirements, but it is clear that the former is the preferred alternative. The methodology used to analyze a large composite structure composed of modular construction elements and to determine the load transfer between composite profiles is described.

Shape Optimization of Holes in Composite Shear Panels

The aim of this work is to find optimum shapes of holes in shear panels made of carbon/epoxy composite materials. The study is restricted to non-buckling shear panels, and a simplified fracture criterion is applied. Starting with a baseline square shear panel with a circular hole, the optimization results in a larger non-circular hole that gives the same maximum stress level in the laminate. Optimum shaped holes are determined for four different laminate configurations, the differences between the shapes being small.

Non-destructive testing of sandwich constructions using thermography

Abstract The concept of sandwich constructions offers many advantages for structures where low weight, high strength and high stiffness are required. The complex build-up of sandwich structures makes, however, quality control difficult. Hence, the development of novel, efficient non-destructive testing methods for such structures is vital. In this paper such a method based on thermography is presented. Thermography with an infrared (IR) scanner has been used to detect prefabricated defects within sandwich panels. The sandwich panels had faces of glass/polyester composite laminates (GRP) and a core of rigid cellular PVC foam. Different types of disbonds were simulated, perpendicular and parallel to the faces. All disbonds were successfully detected and it is particularly interesting that a simulated disbond centred in the core, parallel to the faces, was found. Cavities within the core were also simulated and detected.

Sensitivity analysis of the damage zone model

In this paper a sensitivity study of the Damage Zone Model (DZM) is presented. In the DZM the complex failure state developed in the damage zone at a notch in a composite laminate is modelled as a crack with cohesive forces acting on the crack surfaces. The behaviour of the cohesive forces is assumed to follow an a priori-determined stress-crack opening curve, which is based on the two fundamental parameters: unnotched tensile strength (σ0) and apparent fracture energy (G∗c). The sensitivity in predicted notched strength of specimens with a circular hole, a rectangular hole and cracks is investigated for variations in σ0 and G∗c. Furthermore, an assessment of required finiteelement meshes to obtain convergence is made.

Shape optimization of openings in composite pressure vessels

Abstract To be of any practical use, a pressure vessel must contain openings through which the contents of the vessel may be accessed. It is desired to determine the optimum shape of a hole to be found on the surface of a cylindrical composite pressure vessel subjected to internal pressure and torsion loads in order to reduce the stresses found around these holes. Two materials with quite different physical characteristics, as well as five different layups of the materials, are used in the investigation. The fracture criterion to determine failure around the hole is the Tsai-Hill combined stress factor used in conjunction with the point stress criterion. The OASIS-ALADDIN optimization system, developed at The Royal Institute of Technology, is used to perform the optimization and analyze the results. Results show that the optimum hole shapes are only slightly affected by material properties and laminate geometry.