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On the crack path under mixed mode loading on PUR foams
In this paper are presented the crack initiation angles in polyurethane (PUR) foams under mixed mode loading. Closed cell rigid PUR foams having three different densities 100, 145, and 300 kg/m 3 were investigated. Experiments were performed using Asymmetric Semi-Circular Bend and Single Edge Crack specimens. The obtained crack initiation values were compared with four fracture criteria Maximum Tensile Stress, Strain Energy Density, Maximum Energy Release Rate and Equivalent Stress Intensity Factor, and a good agreement was observed. This allow to conclude that the theoretical fracture criteria developed for solid material could be used with success to predict the crack propagation angles in cellular materials like PUR foams.
Evaluation of mixed mode fracture for PUR foams
Polyurethane foams crush in compression and have a brittle fracture in tension, so their failure could be evaluated based on Linear Elastic Fracture Mechanics. Fracture toughness in mixed mode loading is of particular interest because foam cracking weakens the structure's capacity for carrying loads. Four fracture criteria (Maximum circumferential tensile stress, Minimum strain energy density, Maximum energy release rate, Equivalent stress intensity factor) were considered for evaluation of mixed mode fracture of three closed cell rigid polyurethane foams with densities: 100, 145 and 300 kg/m3. Mixed mode fracture tests were performed using asymmetric semi-circular specimen. The equivalent stress intensity factor criterion looks to give the better prediction of mixed mode fracture. Also the effect of cell orientation and the crack propagation angle were investigated.
Polyurethane foams crush in compression and have a brittle fracture in tension, so their failure could be evaluated based on Linear Elastic Fracture Mechanics. Fracture toughness in mixed mode loading is of particular interest because foam cracking weakens the structure's capacity for carrying loads. The mixed mode fracture of three closed cell rigid polyurethane foams with densities: 100, 145 and 300 kg/m 3 are experimentally investigated. Mixed mode fracture tests are performed using a single edge cracked specimen and a mixed mode loading device. The advantages of this specimen are the simple geometry and the ability to produce full range of mixed modes, from pure mode I to pure mode II, only by changing the loading direction. Fracture criteria based on the cellular topology and tensile strength of the solid material is assessed. It is found that the density of foams is the most important parameter influencing the fracture toughness. The crack propagation angles are also determined on the fractured specimens
Experimental and numerical crack paths in PUR foams
In this paper is presented the behaviour of PUR foams under mixed mode loading. Closed cell rigid PUR foams having three different densities 100, 145, and 300 kg/m 3 were investigated. Experiments were performed using asymmetric semi-circular bend (ASCB) and Assymmetric Four-Point Bend (AFPB) specimens. The obtained crack initiation angles established for ASCB specimens were compared with four fracture criteria MTS, SED, G max and ESIF, and a good agreement was observed. When testing AFPB specimens, and calculating the normalized stress intensity factors it is important to obtain a correct crack propagation, that is to impose proper geometrical dimensions as not to affect the initial crack tip. The eXtended Finite Element Method (XFEM) is a complementary powerful numerical tool used to analyze crack initiation and propagation only if the numerical model is correctly calibrated and all the influencing parameters are properly understood.
Theoretical and Applied Fracture Mechanics, 2017
The Averaged Strain Energy Density (ASED) criteria is applied herein to reinterpret the fracture data of PUR foams. Four type of specimens were used in fracture tests. The ASED parameters were determined based on micromechanical models. The volume control for cracked components is represented by a circle with the centre at the crack tip for all type of fracture modes. It was also demonstrated that the SED parameters obtained from pure mode I could be applied successfully for mixed modes and mode II. This approach represents an useful engineering tool for the assessment of brittle fracture of components made of cellular materials.
Shear and mode II fracture of PUR foams
Polyurethane (PUR) foam materials are widely used as cores in sandwich composites, for packing and cushioning. They are made of interconnected networks of solid struts and cell walls incorporating voids with entrapped gas. The main characteristics of foams are lightweight, high porosity, high crushability, and good energy absorption capacity. Fracture toughness in mixed mode loading is of particular interest because foam cracking weakens the structure's capacity for carrying loads. Present paper assesses the shear elastic (shear modulus) and mechanical (shear strength) properties of polyurethane foams. Also, three different types of specimens were used to determine mode I and mode II fracture toughness. The shear modulus, shear strength and fracture toughness increases with increasing foam density. Also the effect of loading direction and loading speed is investigated. The authors propose a micromechanical model to estimate fracture toughness based on the tensile strength of the solid material and the topology of the cellular structure.
Refinements on fracture toughness of PUR foams
Engineering Fracture Mechanics, 2013
Many efforts have been made in recent years to determine the fracture toughness of different types of foams in static and dynamic loading conditions. Taking into account that there is no standard method for the experimental determination of the fracture toughness of plastic foams different procedures and specimens were used. This paper presents the polyurethane foam fracture toughness results obtained for different foam densities. Two types of specimens were used for determining fracture toughness in modes I, II and a mixed one, and also the size effect, loading speed and loading direction were investigated. The paper proposed correlations for density, cell orientation and mixed mode loading based on the experimental testing results.
This paper presents the effect of loading rate, (ELR), and direction of formation, (DF), of rigid polyurethane foams, (PUR 40 and PUR 140), on fracture toughness. Nominal densities of used foams in the experimental program were 140 kg/m 3 , (for ELS) and 40 kg/m 3 , (for DF), which is closed-cell rigid foams widely used for sandwich cores. Determination of fracture toughness for Mode I fracture of studied materials has made by three-point bending tests, (3PB), on specimens with notches, at room temperature (20 ± 2 ºC). All the specimens were cut from one and the same plate. The specimens were subjected to 3PB at a loading speed of 2 mm/min, except samples for determining the ELR where 2, 20, 200 and 400 mm/min loading speeds were used, and were taken into account the fact that the load must act exactly on the notch direction. All the specimens present brittle failure without plastic deformation.
Iranian Polymer Journal, 2011
T he fracture toughness was determined for cellular polymers by micromechanical modelling using finite element analysis. In this study, mode I and mode II of fracture toughness were evaluated with a 2D-solid model using fracture analysis code FRANC2D/L. Simulation was performed for open cell polyurethane foams of different densities. Two cases were considered: constant cell length, l, and variable cell wall thickness; the former for constant cell wall thickness, t, and the latter for variable cell length. For estimation of fracture toughness the applied loads were progressively increased to the point reaching the fracture strength of the solid material (130 MPa) in an un-cracked strut in front of the crack. The estimated fracture toughness was independent on crack length, indicating that the obtained values could be considered as material property. The values of the fracture toughness of polyurethane foams are in the range of 10 -3 -10 -1 MPa.m 0.5 . Lower values were obtained for mode II fracture toughness. A strong dependency of the fracture toughness on the density of the cellular material was featured by present study. The obtained results for mode I fracture toughness were compared with Gibson-Ashby micromechanical model, by which a good agreement was obtained. While, mode II fracture toughness was compared with Choi and Sankar micromechanical models. The predicted fracture toughness was finally validated with some experimental data. Another advantage of this model was to obtain a fully described the stress field in the solid struts. The stress distribution in the first un-cracked strut showed a combined stress (bending and tension) for mode I loading, while for mode II loading a pure bending appeared.
On fracture toughness of polyurethane foams
2013
Polyurethane (PUR) foam materials are widely used as cores in sandwich composites, for packing and cushioning. They are made of interconnected networks of solid struts and cell walls incorporating voids with entrapped gas, Fig. 1. Of particular interest is the fracture toughness of such foams because foam failure weakens the structure's capacity for carrying loads. Many efforts have been made in recent years to determine the fracture toughness of different types of foams in static and dynamic loading conditions. Micromechanical models and experimental investigations were used for estimating the fracture toughness. This paper presents the polyurethane foam fracture toughness results obtained for different foam densities. Single edge notch bend specimens were tested at room temperature and with different loading speeds. Our results are presented together with other experimental results and correlations related to micromechanical models are made.