Static and Time Dependent Failure of Fibre Reinforced Elastomeric Components. Salim Mirza Element Materials Technology Hitchin, UK

Transcription

1 Static and Time Dependent Failure of Fibre Reinforced Elastomeric Components Salim Mirza Element Materials Technology Hitchin, UK

2 Introduction Fibre reinforced elastomers are used in many applications, such as hoses, tyres, inflatable dams etc. By embedding fibres within the elastomeric layers a composite material is produced that exhibits higher stiffness and strength than elastomer alone. The main mode of failure for fabric reinforced elastomeric components is delamination between the reinforcement layers when subjected to combined tension and shear loads. A failure criterion is presented here, developed through a combination of laboratory scale tests and finite element analysis method, for predicting the time dependent delamination of bonded hoses subjected to static and cyclic loads. Test specimens with multiple fibre reinforced layers were developed. Local conditions in the specimens were obtained using FEA. Failure criterion was defined based from the experimental and numerical results.

3 Experimental Programme Test Specimen Design: Shear 1 layers of fabric reinforcements embedded in Rubber (different types and ply angles) 75mm Second Rubber Layer Liner Rubber 36mm Steel

4 Experimental Programme Test Setup: In different modes of loading (a) Shear (b) Shear/Peel (c) Peel

5 Force (N) Force (N) Force (N) Experimental Programme Static Tests: To assess different designs Displacement (mm) (a) Shear tests different designs M3 S2 OLD 1 M3 S2 OLD 2 M3 S2 OLD 3 M4 S3 OLD 1 M4 S3 OLD 2 M4 S3 OLD 3 M5 S4 OLD 1 M5 S4 OLD 2 M5 S4 OLD 3 M6 S5 OLD 1 M6 S5 OLD 2 M6 S5 OLD 3 Shear/Peel Peel Displacement (mm) M14 - SP1-1 M14 - SP1-2 M14 - SP1-3 M15 - SP2-1 M15 - SP2-2 M15 - SP2-3 M16 - SP3-1 M16 - SP3-2 M16 - SP Displacement (mm) M14 - P1-1 M14 - P1-2 M14 - P1-3 M15 - P2-1 M15 - P2-2 M15 - P2-3 M16 - P3-1 M16 - P3-2 M16 - P3-3 (b) Tests to assess influence of thickness

6 Experimental Programme Static Tests: Failure location and Initiation in different modes of loading (a) Shear tests (b) Shear/Peel (c) Peel

7 Experimental Programme Static Tests: Variation in location of failure for different systems. (c) Peel (a) System A (b) System B

8 Displacement (mm) Experimental Programme Time to Failure Tests: Constant force tests Physical creep/crack initiation 5 3. Crack growth /total failure 1. Loading Time (minutes) C1 S5 1 45N Hold C2 S5 2 3N Hold C2 S5 3 22N Hold C2 S5 4 22N Hold C2 S5 6 19N Hold C1 S5 1 3N Hold C1 S5 2 22N Hold C1 S5 3 19N Hold C1 S N Hold C4 S5 4 3N Hold C4 S N Hold

9 Displacement (mm) Displacement (mm) Displacement (mm) Experimental Programme Cyclic Tests : H3 S3 5 32N Durability 1 cycle / hour 15 H5 S3 3 32N Durability 1 cycle / hour H5 S3 3 32N Durability 1 cycle / hour 1 5 H4 S N Durability 1 cycles / hour H4 S3 2 45N Durability 1 cycles / hour H4 S N Durability 1 cycles / hour 15 H4 S3 3 4N Durability 1 cycles / hour H5 S3 2 4N Durability 1 cycles / hour H5 S N Durability 1 cycles / hour H5 S N Durability 1 cycles / hour H5 S3 3 32N Durability 1 cycles / hour Time (minutes) Time (minutes) Time (minutes) (a) 1 cycle/hour (b) 1 cycle/hour (c) 1 cycle/hour

10 Finite Element Analysis Modelling of fabric reinforced elastomers Options available Each fibre modelled as discretely Composite layers can be modelled as homogeneous layer using orthotropic material models assuming linear elastic response Represent fibre as Rebar elements embedded into the elastomeric layers. Different types of rebar elements available.

11 Load (N) Finite Element Analysis: Shear Test Shear Test Method 1: Number of fabric layers are represented as one layer and material properties and orientations of each layer are defined in the material definition. One membrane layer is used to represent multiple fabric reinforcements Test#1 Test#2 Test#3 Model-Method1 2 Rubber Second Rubber Layer Experiment Displacement (mm) FE Model Liner Rubber Steel

12 Load (N) Finite Element Analysis Shear Test - Method 2: Each fabric reinforcement layer is defined individually and assigned respective material properties and orientations. Fabric Reinforcement Layers Embedded in Rubber 12 1 Test#1 Test#2 Test#3 Model-Method x Layers at o 4 x Layers at 45 o Second Rubber Layer Liner Rubber Experiment Displacement (mm) FE Model Steel

13 Load (N) Finite Element Analysis: Shear/Peel Test Shear/Peel Test Test #1 Test #2 Test #3 FE Model Displacement (mm) Finite Element Model Comparison of Predicted and measured load displacement response

14 Load (N) Finite Element Analysis: Peel Test Peel Test 2 Test #1 Test #2 15 Test #3 FE Model Displacement (mm) Finite Element Model Comparison of Predicted and measured load displacement response

15 Load (N) Finite Element Analysis Modelling Delamination: Cohesive Elements/Zone 1 8 Test#1 Test#2 Test#3 FE Model 6 4 Failure Initiation Displacement (mm) Complete Failure Predicted delamination and measured response

16 Force (N) Failure Criterion Definition Experimental Relationship Between Time to Failure and Load Represented by a power law with an exponent that was characteristic of the system and independent of the mode of loading Cyclic loading was found to cause additional damage compared with the constant load 1 y = 514.5x -.61 Static Data Constant Force y = x -.8 Constant Force Runouts Durability 1 cycle/hour Durability 1 cycle/hour Durability 1 cycle/hour Time to failure initiation (minutes)

17 Load (N) Strain Failure Criterion Definition Good agreement was obtained between the measured and predicted deformed shapes and load/displacement responses which provided validation of the models. Local stresses and strains were derived from FEA of the test pieces Test #1 Test #2 Test #3 FE Model-Load FE Model-Strain Displacement (mm) Predicted Strain Distribution Predicted Load and Maximum Strain as a Function of Displacement

18 Maximum principal strain (%) Failure Criterion Definition Maximum principal strain (e p ) in the layer where failure occurred was used to define time to failure (t f ) and following relation was found: Constant Force: 1 Pull to failure t f = ε f y = x -.45 constant force 1 Cycle / hour 1 Cycles / hour Dynamic Force: y = x Cycles / hour t f = ε f Time to failure (minutes)

19 Failure Criterion Validation Model Hose Section Test Specimen Model hose section test Specimen representing the geometry and lay-up round a hose end-fitting was designed to validate the failure criterion developed The test piece consisted of a pair of beads that could be tested in parallel with clamping to replicate the constraining effect of binding wires. Bondline Schematic of Model Hose Section Test Specimen as Moulded

20 Force (kn) Failure Criterion Validation Model Hose Section Test Specimen: Static and Cyclic Tests 1 Close correlation was found between the shear test piece and model hose section test specimen Model Hose Pull to Failure Model Hose Constant Force Model Hose 1cycles/hour Shear Test Pull to Failure Shear Test Constant Force Shear Test 1 cycles/hour Test Set Up Time (minutes)

21 Force (kn) Force (kn) Failure Criterion Validation Finite Element Analysis of Model Hose Section Test Specimen: Comparison of Predicted time to failure and experimental data 1 Experiment Pull to Failure Experiment Constant Force Predicted - friction.15 Predicted - friction.6 1 Experiment 1 cycles/hour Predicted - friction.15 Predicted - friction.6 Lower End Fixed Time (minutes) Time (minutes) Pull Finite Element Model Constant Load Cyclic Load

22 Conclusions A failure criterion has been developed from laboratory scale tests and finite element analysis for predicting the ultimate strength and time to failure under static and cyclic loads. The failure criterion has been validated by comparing the predicted time to failure for a model hose test piece with experimental data. The laboratory scale test pieces provide a means of assessing the properties of a system of materials consisting of bonding systems, elastomeric layers and fibre reinforced layers, where it may not be known before hand which may be the weakest layer or interface where failure may occur. It has been demonstrated that finite element analysis is a valuable tool for providing accurate assessment of the behaviour of fabric elastomeric components e.g. bonded hoses.