MECH 5312 – Solid Mechanics IIDr. Calvin M. Stewart

Department of Mechanical Engineering

The University of Texas at El Paso

Table of Contents

• Failure of Components

• Fracture Mechanics

• Modes of Fracture

• The Stationary Crack• Blunt Crack

• Sharp Crack

• Crack Propagation and the Stress Intensity Factor

• Fracture: Other Factors

Failure of Components

• Failure by excessive deflection• Elastic deflection

• Deflection caused by creep

• Failure by general yielding

• Failure by fracture• Sudden failure of brittle materials

• Fracture of cracked or flawed members

• Progressive fracture (fatigue)

• Failure by instability The DeHavilland Comet Crash – Progressive Fracture

Fracture Mechanics

• Fracture – field of study focused on characterizing the behavior of cracks in cracked structures.

• Notes:• Understanding how crack behaves equips engineers with the tools needed to

design against the initiation and propagation of cracks

• Fracture behavior is dependent on material, load/displacement, and geometric factors

Modes of Fracture

, ,I II IIIK K K

The Stationary Crack

• Elliptical Hole

The Stationary Crack

• Elliptical Hole

• Stress Concentration Factor

• Rho is the radius of curvature

2b

a

The Stationary Crack

• The challenge as the crack sharpens

100 1 2 100 201

1000 1 2 1000 2001

1 2

cc

cc

cc

aS

b

aS

b

aS

b

Challenge!!!

Analytical Solution to Stress in Blunt Crack

• Blunt Crack with radius of curvature

2b

a

Analytical Solution to Stress in Sharp Crack

• Sharp Crack b->0

• Stress Intensity Factor

• Check for Fracture

Stress Intensity Factor, KI

• The Stress Intensity Factor, KI remains finite while the Stress Concentration Factor, Scc becomes infinite!!!

• Definition: The Stress Intensity Factor (SIF) is a fracture mechanics parameter used to characterize the strength of the singularity at the crack tip, denoted by K.

• The subscripts I,II, or III correspond to the opening, sliding, and tearing modes of fracture, respectively.

• The Stress Intensity Factor, KI is dependent on geometry and loading condition.

Fracture Toughness

• Definition: The Critical Fracture Toughness is a cracked material’s ability to resist fracture, denoted by KC. It is considered a material property and commonly used in design.

• Units are or1.099ksi in MPA m

ksi in MPA m

No Fracture

Fracture

I IC

I IC

K K

K K

Griffith’s Energy Approach

• Griffith introduced the concept of strain energy release rate, G.

• The quantity G represents the amount of strain energy lost by the member per unit area of the newly formed crack as the crack propagates.

• G may be written [F/L], G is referred to as the crack extension force.

• Related to the Stress Intensity Factor, K as follows

Plane Stress (thin) Plane Strain (thick)

Griffith’s Energy Approach

• The Plane Strain Critical Strain Energy Release Rate, GIC follows

The Plane Strain Fracture Toughness, KIC follows

where in both cases, there exists a critical crack length, ac that in combination with the applied load, σ cause fracture!

Thickness-DependenceIncreasing Uncertainty

Plane Strain Requirement

where a is the initial crack length and t is the thickness sometimes reported as B, and Y is the yield strength.

Common ASTM Standards for Fracture

• ASTM E1820 Standard Test Method for

• Measurement of Fracture Toughness

• ASTM E399 Standard Test Method for Plane-Strain Fracture Toughness of Metallic Materials

Temperature-Dependence of KIC

Stress Intensity Factors, SIFs

• The Analytical Solution to the Stress Intensity Factors, K can be determined using various analytical techniques

• The Solutions to many problems including• 2D or 3D Geometry

• Boundary Conditions

• Have been achieved

• Many Books & Software

Fracture: Other Factors

• Elastic-Plastic Fracture Mechanics

• Crack-Growth Analysis

• Load Spectra and Stress History

• Others

A Plastic Zone develops ahead of the Crack Tip

Load-Controlled Fatigue Crack Growth

Example

Calvin M. StewartAssistant ProfessorDepartment of Mechanical EngineeringThe University of Texas at El Paso500 W. University Blvd.Suite A126El Paso, Texas 79968-0717

Email: cmstewart@utep.eduURL: http://me.utep.edu/cmstewart/Phone: 915-747-6179Fax: 915-747-5019

Contact Information