# Ch.8 Failure

## 8.1 Introduction

- Failure of engineering materials is almost always undesirable because it endangers human life, causes economic loss, and interrupts products and services.
- Even if the causes of failure and material behavior are understood, failures are still hard to completely prevent due to improper material selection and processing, inadequate design, or misuse.
- Engineers must anticipate possible failures and, when they occur, analyze the causes and implement measures to prevent recurrence.

### Topics in this chapter

- Simple tensile fracture: ductile and brittle modes.
- Fundamentals of fracture mechanics and fracture toughness testing.
- Ductile-to-brittle transition behavior.
- Fatigue and creep: mechanisms, testing, and prevention.

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## 8.2 Fundamentals of Fracture

- Simple fracture is the separation of a body into two or more pieces under a nearly static stress at a temperature low compared with the melting point.
- Failure can be caused by tension, compression, shear, or torsion, but the discussion mainly focuses on uniaxial tensile fracture.

### Ductile vs brittle fracture

- Ductile fracture shows significant plastic deformation and high energy absorption before fracture, usually providing warning.
- Brittle fracture exhibits little or no plastic deformation, low energy absorption, and rapid catastrophic crack propagation with no warning.
- Ductility is quantified by percent elongation and percent reduction in area, and depends on temperature, strain rate, and stress state.

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## 8.3 Ductile Fracture

### Ductile fracture process (cup-and-cone)

1) Necking begins in the specimen.
2) Small internal cavities (microvoids) form within the necked region.
3) Microvoids grow and coalesce into an elliptical crack whose major axis is perpendicular to the tensile direction.
4) The crack extends along its major axis and finally propagates rapidly around the neck at about 45° to the tensile axis, producing a cup-and-cone fracture surface.

### Ductile fracture surface features

- Macroscopic: a central fibrous region (intense plastic deformation) surrounded by a shear lip region.
- Microscopic (SEM):
- Under uniaxial tension: many roughly spherical dimples, each corresponding to a microvoid.
- Under shear: elongated or parabolic-shaped dimples on the shear lip, indicating shear failure.
- Fractography provides information on fracture mode, stress state, and crack initiation site.

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## 8.4 Brittle Fracture

### Brittle fracture characteristics

- Brittle fracture occurs with negligible plastic deformation and very rapid crack propagation.
- The crack path is nearly perpendicular to the tensile stress direction, producing a relatively flat fracture surface.

### Brittle fracture surfaces

- Macroscopic patterns:
- V-shaped chevron markings that point back to the crack origin.
- Radial, fan-shaped ridges that emanate from the crack initiation site.
- Microscopic modes:
- Transgranular (cleavage): crack cuts through grains along crystallographic planes; surface looks faceted or grainy.
- Intergranular: crack propagates along grain boundaries, often due to grain-boundary weakening or embrittlement.

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## 8.5 Principles of Fracture Mechanics

### Stress concentration and crack tips

- Small cracks and flaws exist in all materials, making measured fracture strengths much lower than theoretical values.
- Cracks and notches cause large local stress amplification at their tips, and sharper cracks produce higher stress concentration.

### Energy criterion (Griffith concept)

- In brittle materials, fracture occurs when the stress at the crack tip reaches a critical value or when the release of elastic strain energy balances the energy needed to create new surfaces.
- The critical stress depends on crack half-length \(a\), surface energy, and elastic modulus, so the largest and most highly stressed cracks fail first.

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## Stress Intensity and Fracture Toughness

### Stress intensity factor K

- The stress intensity factor \(K\) characterizes the stress field near a crack tip and depends on load, crack size, and geometry.
- For mode I (opening mode), \(K\) is often written in the form \(K = Y\sigma\sqrt{\pi a}\), where \(Y\) is a dimensionless geometry factor.

### Fracture toughness Kc and KIc

- Fracture toughness \(K_c\) measures a material’s resistance to brittle fracture in the presence of a crack.
- Under plane strain (thick specimens) in mode I, the toughness is denoted \(K_{Ic}\) and is essentially independent of thickness.
- Ductile materials generally have high \(K_{Ic}\) values, while brittle materials have low \(K_{Ic}\).

### Design and critical crack length

- If \(K_{Ic}\) and the maximum allowable crack size are known, a safe working stress can be chosen to avoid fast fracture.
- If \(K_{Ic}\) and the service stress are fixed, one can compute the maximum tolerable crack length; larger cracks must be repaired or removed.
- The critical crack length is a measure of a material’s damage tolerance.

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## Stress Concentration and Design

- The theoretical stress concentration factor \(K_t\) depends only on geometry (holes, notches, fillet radii).
- In ductile metals, yielding at the stress raiser redistributes stress and reduces the effective concentration below the theoretical value.
- Brittle materials lack such plastic redistribution, so the full theoretical stress concentration is realized; sharp corners should be avoided and replaced by smooth fillets.

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## Toughening and Embrittlement

### Toughening by fibers

- Polymers alone often behave similarly to ductile metals, but fiber-reinforced polymer composites show different fracture behavior.
- As a crack grows in the matrix, fibers can remain intact and bridge the crack, acting as crack stoppers and increasing energy absorption.

### Embrittlement mechanisms

- Impurities in alloys tend to segregate to grain boundaries, creating a low-toughness network that promotes brittle intergranular fracture.
- Chemical environment or high temperature can further weaken boundaries, turning normally ductile materials brittle.

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## Ductile-to-Brittle Transition and Impact Testing

### Impact test conditions

- Charpy impact tests use notched specimens under high loading rate and low temperature to promote brittle fracture.
- The impact energy is obtained from the difference between the pendulum’s initial and final heights and reflects the material’s toughness at that temperature.

### Ductile-to-brittle transition (DBTT)

- Some BCC metals (such as low-strength steels) change from ductile to brittle behavior as temperature decreases.
- Plotting impact energy versus temperature reveals a transition region; the DBTT is used to define safe operating temperature ranges.
- Historical failures (e.g., ship hulls and welded structures) illustrate brittle fracture of steels that appear ductile in normal tensile tests.

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## Fatigue

### Basic concept

- Fatigue failure occurs under repeated or cyclic loading even when the maximum stress is below the yield strength.
- Fatigue is responsible for the majority of mechanical engineering failures.

### S–N curve and fatigue life

- An S–N curve plots stress amplitude \(S\) versus the logarithm of cycles to failure \(N\).
- Many steels show a fatigue limit \(S_{fat}\), below which failure does not occur regardless of cycles.
- Materials such as aluminum typically have no true fatigue limit; only a fatigue strength for a specified life can be defined.

### Improving fatigue life

1) Reduce mean stress: for the same stress amplitude, lower mean stress increases fatigue life.
2) Surface treatments:
- Shot peening introduces compressive residual stress at the surface, suppressing crack initiation and growth.
- Carburizing hardens the surface and induces compressive stress by diffusing carbon into the outer layer.
3) Design changes: remove or smooth stress raisers, e.g., replace sharp corners with rounded transitions.

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## Creep

### Concept and three stages

- Creep is time-dependent plastic deformation under constant stress at elevated temperature, typically for metals when \(T \gtrsim 0.4 T_m\) (absolute).
- A typical creep curve (strain vs. time) shows:
- Primary creep: decreasing creep rate due to work hardening.
- Secondary creep: steady-state creep with nearly constant creep rate, important for design.
- Tertiary creep: accelerating creep rate leading to rupture due to damage accumulation and reduced cross-section.

### Temperature and stress effects

- The steady-state creep rate increases with both temperature and applied stress, and depends on material parameters such as stress exponent and activation energy for creep.
- Creep rupture life decreases as temperature and stress increase, so high-temperature components must be designed for long-term creep resistance.

### Larson–Miller parameter

- Long-term creep data are impractical to obtain directly, so the Larson–Miller parameter \(m = T(C + \log t_r)\) combines temperature and rupture time into a single variable.
- Using high-temperature, short-time data, engineers can extrapolate to predict long-time rupture life at lower temperatures.

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## Key Points

- Small cracks and flaws are unavoidable; stress concentration and fracture mechanics control actual failure strength.
- Fracture toughness and stress intensity factors are central to designing cracked components by setting allowable stresses or allowable crack sizes.
- Fatigue governs failures under cyclic loading, and creep governs high-temperature, long-term deformation; both require appropriate design curves.
- Geometric design, surface treatments, and proper material selection are critical for avoiding sudden brittle failure and extending service life.