01_INTRODUCTION_TO_FRACTURE_MECHANICS_linkedin

Ozen Engineering Inc.

1210 E. Arques Ave, Suite 207

Sunnyvale, CA 94085

info@ozeninc.com

Can Ozcan (can@ozeninc.com)

Fracture Mechanics in Ansys R16

Session-01

Introduction to Fracture

Mechanics

Design Philosophies

• It is critical to decide on a design philosophy

– Safe-Life

– Fail-Safe

– Damage-Tolerant

22

What is Fracture Mechanics?

• It is the study of flaws and cracks in materials

• Can be seen as a special case among different design philosophies

• Mostly deals with crack growth and life-time estimation

23

Why is Fracture Mechanics important?

• Strength of Material approach does not anticipate the presence of a crack or does via concentration factors

• Presence of cracks can significantly decrease the structural strength and reliability

4

𝜎 =𝐹

𝐴𝜎 ≫

𝐹

𝐴

4

Why is Fracture Mechanics important?

• Flaw Size (a) is an important parameter in fracture mechanics approach

• Fracture Toughness replaces strength of material

5

𝜎 ≫𝐹

𝐴

a

– For Linear-Elastic Fracture Mechanics (LEFM), fracture toughness of a material is determined from “Stress Intensity Factor”

– For Elastic-Plastic Fracture Mechanics(EPFM), fracture toughness is determined via energy required to grow a crack

𝑲𝑰𝑪

𝑱𝑰𝑪

5

Industries

• Probably encountered in any industry dealing with structures

– Automotive

– Electronics

– Healthcare

– Aviation

– Civil

– Nuclear

– Defense

– Maritime

6

Historical Background

• Comet Airplanes

7

[1] “The DeHavilland Comet Crash | Aerospace Engineering Blog.” [Online]. Available:

http://aerospaceengineeringblog.com/dehavilland-comet-crash/. [Accessed: 17-Mar-2015].

Historical Background

• Liberty Ships

• ~1,500 instances of brittle fracture during WWII

• Studies revealed ships in North Atlantic were exposed to cold temperatures were subject to brittle fracture

8

Effect of Temperature on Fracture Toughness

• Fracture Toughness of materials are affected by temperature

• Ships experiencing cold weather conditions may be prone to fracture type failures

9

Historical Background

• Aloha Flight #243 in 1988:

• German Train ICE Accident in 1998:

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• Life span definition:

Crack Initiation & Propagation

11

• Life span definition for fatigue analysis:

Crack Initiation & Propagation

The initiation stage can represent a large part of the life span

During the stable propagation stage the crack speed grows exponentially with the

crack size

The crack grows unstably until the ductile fracture

Simulation context

12

CRACK INITIATION

• Physically, cracks initiate from;

– An imperfection

– An already existing crack

– A damaged (locally weakened) area

• A failure analysis must include;

– Stress analysis

– Failure criterion

13

Theoretical Developments

• A. Griffith (1893-1963) published the results of his studies on brittle fracture

• He found the strength of glass depended on the size of microscopic cracks

CONSTANTaS

14

15

Three Modes of Fracture

• Mode I denotes a symmetric opening (opening or tension mode)

• Mode II denotes an antisymmetric separation (In-plane shear mode)

• Mode III denotes an antisymmetric separation (out-of-plane shear or tearing mode)

• Crack growth usually takes place in mode I or close to it.

• The crack “adjusts” itself such that the load is perpendicular to the crack faces.

16

Fracture Mechanics Parameters

• J-Integral

• Energy-Release Rate

• Stress-Intensity Factor

• T-Stress

• Material Force

• C*-Integral

– UMM Method (Unstructured Mesh)

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Energy Release Rate and J-Integral

Energy release rate can be calculated from stress intensity

factors

The J-integral can be defined as a path-independent line

integral that measures the strength of the singular stresses

and strains near a crack tip.

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18

Stress Intensity Factor

• The magnitude of stress field in the immediate vicinity of the crack tip is measured by the “Stress Intensity Factor”

• Stress Intensity Factor is a quantity determined analytically and varies as a function of the crack configuration and the external loads are applied

• Critical stress intensity factor is independent of the crack geometry and loading and may be regarded as a material constant.

• Typical critical stress intensity factor values are;Ultimate Critical StressStrength Intensity Factor

• AL 7075-T651 83 ksi 26 ksi in1/2

• AISI 4340 280 ksi 40 ksi in1/2

19

T-Stress

• Is the stress acting parallel to the crack faces

• Unlike J-integral, it can have both negative and positive values

• Positive T-stress values promotes fracture, where negative T-stress values results in larger plastic zones)

20

Material Force

• “Material Force” method provides parameters for global material and dissipation forces that yield near-tip crack-driving force

• Can be applied to all kind of material models (elastic, visco-elastic, plastic…)

21

C*-Integral

• Creep crack growth becomes a concern when structural components are operated at high temperatures (ie Nuclear Industry)

• C*-Integral can be used to evaluate the crack tip fields under creep deformation

• C*-Integral is a path-independent integral, which is the steady-state creep analogue of J integral.

22

UMM Method

• The unstructured mesh method (UMM) is a numerical tool used for evaluating fracture mechanics parameters on unstructured hex or tet element meshes.

• Unstructured mesh method supports:

– J-integral

– Stress-intensity factor

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Fracture Mechanics Table

• Which parameters is applicable for which assumptions:

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Method Material Behavior

J-Integral Linear isotropic elasticityIsotropic plasticity

Energy-Release Rate(VCCT Method)

Linear isotropic elasticityOrthotropic elasticityAnisotropic elasticity

Stress-Intensity Factor Linear isotropic elasticity

T-Stress Linear isotropic elasticityIsotropic plasticity

Material Force Various (including plasticity,viscoelasticity)

C*-Integral Creep

Crack-Growth Simulation

• VCCT-Based Interface Element Method

• Cohesive Zone Method

• XFEM-Based Method

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Fracture Mechanics Meshing & Element Support

KSCON command is used to skew

mid-side nodes around the crack tip.

This way the crack tip 1/(r1/2)

singularity is captured.

PLANE183

SKEWED NODES

SOLID186

PLANE183

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Fracture Mechanics Meshing & Element Support

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2-D Edge Crack Propagation

2 D Edge cracked plate

analysis

can be solved both using

fracture mechanics tools

and cohesive zone

elements in ANSYS.

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2-D Edge Crack Propagation

Crack Propagation Animation, β =15° (a) Crack Propagation Path, (b) SIF, FI; β =15°

• Fracture parameters can be calculated directly using KCALC and CINT command in ANSYS.

• Crack initiation angle and energy release rate can be calculated from stress intensity factors.

• Cracks propagate straight (parallel to loading direction) to attain pure mode-I conditions.

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29

Interface modeling

Problem Geometry Finite Element Model

Edge crack propagation in a thin film-substrate(SiO2/Si) is studied.

Effect of interface layer on crack propagation path is examined using cohesive zone elements.

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30

3-D Edge Crack Analysis

In Thin Film-Substrate Systems

(a) Propagation Animation; Cut

Length=150

(b) Propagation Path; Cut Length=150

Crack propagation is performed quasi-statically. Fracture parameters are calculated

at each propagation step and the geometry is updated for the next propagation step.

Cohesive zone elements are placed between thin film and substrate to model

interface.

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31

Industrial Example: Pump Housing Fracture

• Pump housing subjected to internal pressure with a through crack

Crack

0

0.04

0.08

0.12

0.16

0 1 2 3 4

Path 1

Path 2

Path 3

Path 4

Path 5

Inner surface

Outer surface

J Integral

Calculations

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Industrial example: Cracked helicopter flanged plate

• Automatic crack growth simulation under variable loading

33

Following Week Schedule

• March 26th: 10AM-10:45AM PT How to Perform Fracture Mechanics Analysis in Workbench

• April 2nd: 10AM-10:45AM PT XFEM Method –Meshless Fracture Mechanics

• April 9th: 10AM-10:45AM PT Fracture Mechanics with Cohesive Zone and Delamination

• April 16th: 10AM-10:45AM PTFatigue Crack Propagation

34

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END

Thanks for your attention !!!

Questions ?

CONTACT:Attention: Can Ozcan

OZEN ENGINEERING, INC.

1210 E. ARQUES AVE. SUITE: 207

SUNNYVALE, CA 94085

(408) 732-4665

info@ozeninc.com

www.ozeninc.com