Fracture Mechanics. External Course Siemens. Winter

Transcription

1 Fracture Mechanics External Course Siemens Winter Lars Damkilde Division for Structures, Materials and Geotechnics Department of Civil Engineering, Aalborg University 1 Presentation Background in Structural Mechanics, Applied Mechanics Lic. Techn in Stability Problems (equivalent to Ph.D) Theoretical and practical experiences in FEA (linear and non-linear) Teaching experiences from 15 years at DTU and 10 years at AAU Published a large number of journal papers At present Head of Division for Structures, Materials and Geotechnics at Department of Civil Engineering and Professor in Structural Mechanics. 2 1

2 Course in Fracture Mechanics Complicated to choose the approach Basic theory Continuum Mechanics Mathematics Overview Examples Only a general approach Fracture/Fatigue In practise very tight connection 3 Outcome of course General knowledge Theory kept at minimum Identification of important factors in both fracture and fatigue analysis Analysis based on Finite Element approach Hands on Practical approach How to investigate fracture/fatigue in practise Modelling Interpretation of results 4 2

3 Outline of course The course are divided into 4 blocks General introduction Finite Element Fatigue Advanced topics 5 What is fracture? In the following material has been taken from Wikipedia: A fracture is the (local) separation of an object or material into two, or more, pieces under the action of stress. Brittle failure Ductile failure 6 3

4 Ductile failure Materials: Steel, reinforced concrete, clay. 7 Ductile failure Characteristics: - No sudden processes - The stress level are constant in a long interval - Large strains distributed over a larger volume - Material behaves plastic 8 4

5 Analysis of ductile failure Relative uncomplicated Failure can be identified by the global stress level Advanced ductile failure analysis involving large strains is seldom of interest. Analysis of explosion resistance. Deep drawing of components. 9 Brittle failure Example: Glas - Very localized strains/dislocations - Irreversible proces - Sudden proces - Initiation of cracks depends on local imperfections and local stress level 10 5

6 Focus: Brittle failure Analysis is much more complicated Failure depends on local stress level Failure depends on local imperfections Microcracks Composite structure Results will have more scatter Strength parameters may depend on size of structure 11 Ductile/brittle failure are connected Fracture of an Aluminum Crank Arm. Bright: Brittle fracture. Dark: Fatigue fracture. 12 6

7 Brittle failure analysis of stress around local cracks All stresses will go to infinity close to a sharp edge regardless of load, geometry, material etc. Can be shown theoretical but try yourself on a Finite Element Model Refinement will lead to larger stresses. A stress based fracture criterion is of no physical relevance. Something new has to be defined. 13 FEM simulation of plate in plane stress. Load and geometry 14 7

8 Displacement Mode I 15 Stresses become large close to crack tip 16 8

9 Normal stresses near crack tip go to infinity 17 FEM task Consider a quadratic steel plate in plane stress. Dimensions side 200 mm, thickness 1 mm The load results in pure tension in one direction. Define a crack in the center of the plate of length 5 mm. Calculate the stress state near the crack tip for different meshes and show that the stress will go to infinity. Load the plate in pure shear and show the same. 18 9

10 Brittle failure new material parameter Fracture thoughness Sharpy test: 19 Apparatus The Sharpy test measures the loss of kinetic energy. The loss of kinetic energy is taken as a measure of the materials resistance towards fracture. For all materials there are a critical level of strain energy per volume. If the critical level is reached the material will separate (crack)

11 Fracture thoughness Fracture thoughness depend on: Material decomposition Temperature In materials science, fracture toughness is a property which describes the ability of a material containing a crack to resist fracture, and is one of the most important properties of any material for virtually all design applications. The fracture toughness of a material is determined from the stress intensity factor (K) at which a thin crack in the material begins to grow. 21 Fracture Mechanics Fracture mechanics is the field of mechanics concerned with the study of the propagation of cracks in materials. It uses methods of analytical solid mechanics to calculate the driving force on a crack and those of experimental solid mechanics to characterize the material's resistance to fracture. Technical questions to be answered: Is a given crack geometry/size stable or not for a given load? In which direction will the crack propagate? 22 11