8.3 Fatigue, creep, and impact loading

Fatigue, Creep, and Impact Loading

Fatigue, creep, and impact loading are three ways materials can fail that don't show up on a simple stress-strain curve. A part can break well below its ultimate tensile strength if it's loaded repeatedly, held at high temperature, or struck suddenly. Understanding these failure modes is essential for designing components that survive real-world service conditions.

Fatigue Failure Mechanisms

Fatigue Crack Initiation and Propagation

Fatigue failure happens when a material is subjected to repeated or fluctuating stresses below its ultimate tensile strength. Over many cycles, microscopic cracks form and grow until the part breaks. The process unfolds in two stages:

1. Crack initiation. Tiny cracks nucleate at stress concentration sites: surface scratches, machining marks, inclusions, or grain boundaries. These are the weakest links where localized plastic deformation accumulates cycle after cycle.
2. Crack propagation. Once a crack has formed, each loading cycle opens and extends it slightly. The crack grows steadily until the remaining cross-section is too small to carry the applied load. At that point, final fracture occurs suddenly.

The dangerous part of fatigue is that both stages can happen with no visible warning. The component looks fine right up until it doesn't.

Factors Affecting Fatigue Life

Fatigue life is the number of stress cycles a component can withstand before failure. Many variables influence it:

• Stress amplitude and mean stress. Higher stress amplitude shortens fatigue life dramatically. A tensile mean stress also reduces life compared to fully reversed loading.
• Stress ratio $R = \frac{\sigma_{min}}{\sigma_{max}}$. This describes the nature of the loading cycle. An $R = -1$ cycle is fully reversed (equal tension and compression). As $R$ increases toward +1, the loading becomes more tensile-dominated, which generally reduces fatigue life.
• Material properties. Higher strength and ductility both help, though they trade off against each other. Notch sensitivity matters too: a high-strength steel may be more sensitive to small defects than a tougher, lower-strength alloy.
• Surface condition. Rough surfaces, corrosion pits, and sharp geometric features all act as crack initiation sites. Surface treatments like shot peening (which introduces compressive residual stresses) and case hardening can significantly extend fatigue life.
• Environment. Elevated temperature, corrosive media, and fretting (small relative motion between contacting surfaces) all accelerate fatigue damage.
• Loading frequency and load history. Variable-amplitude loading is harder to analyze than constant-amplitude loading and requires cumulative damage methods.

S-N Curve Interpretation

S-N Curve Characteristics

An S-N curve (also called a Wöhler curve) plots stress amplitude $S$ on the vertical axis against the number of cycles to failure $N$ on the horizontal axis. Both axes typically use a logarithmic scale.

• For ferrous metals (steels, cast irons), the curve often flattens out at high cycle counts. The stress level where it flattens is the endurance limit (or fatigue limit): below this stress, the material can theoretically survive an infinite number of cycles. For most steels, the endurance limit is roughly 40–50% of the ultimate tensile strength.
• For non-ferrous metals (aluminum, copper alloys), the S-N curve keeps sloping downward and never truly flattens. These materials don't have a true endurance limit, so engineers define a fatigue strength at a specified number of cycles (commonly $10^7$ or $10^8$).

S-N curves are generated from laboratory tests on polished, carefully prepared specimens under controlled conditions. Real components differ from lab specimens, so modifying factors are needed.

Fatigue Life Prediction Using S-N Curves

To use an S-N curve for design:

1. Determine the stress amplitude the component will experience in service.
2. Apply modifying factors to account for differences between the lab specimen and the real part. Common factors include surface finish, size, reliability level, and stress concentration (notch factor $K_f$).
3. Locate the adjusted stress amplitude on the S-N curve and read across to find the predicted number of cycles to failure.

For variable-amplitude loading, where the stress level changes over time, use Miner's rule (Palmgren-Miner linear damage hypothesis). The idea is straightforward: each block of cycles at a given stress level uses up a fraction of the fatigue life. Failure is predicted when the sum of all damage fractions reaches 1:

$\sum \frac{n_i}{N_i} = 1$

where $n_i$ is the number of cycles applied at stress level $i$ and $N_i$ is the number of cycles to failure at that stress level from the S-N curve. Miner's rule is simple but approximate; it ignores load sequence effects.

For components under combined static and cyclic loading, the Goodman diagram and Soderberg diagram are used. These plot alternating stress against mean stress and define a safe operating region. The Goodman line connects the endurance limit on the alternating stress axis to the ultimate tensile strength on the mean stress axis. The Soderberg line is more conservative, using the yield strength instead.

Creep Behavior of Materials

Creep Stages and Mechanisms

Creep is time-dependent permanent deformation that occurs under sustained load at elevated temperatures. As a general guideline, creep becomes significant above roughly $0.4 \, T_m$, where $T_m$ is the material's absolute melting temperature in Kelvin. For steel ($T_m \approx 1800 \, K$), that's about 720 K (roughly 450°C). For lead ($T_m \approx 600 \, K$), creep occurs near room temperature.

A typical creep curve (strain vs. time at constant stress and temperature) has three distinct stages:

1. Primary creep. The strain rate starts high and gradually decreases. The material is strain hardening, which makes further deformation progressively more difficult.
2. Secondary creep (steady-state creep). The strain rate reaches a constant, minimum value. Strain hardening and thermal recovery processes are in balance. This stage usually occupies the longest portion of the creep life, and the steady-state creep rate is the most important parameter for design.
3. Tertiary creep. The strain rate accelerates as internal voids nucleate and grow, the cross-section necks down, and the material weakens. This stage ends in rupture.

The dominant creep deformation mechanisms depend on stress and temperature:

• Dislocation glide and climb at higher stresses
• Grain boundary sliding at intermediate conditions
• Diffusional flow at lower stresses and higher temperatures: Nabarro-Herring creep (diffusion through the grain interior) and Coble creep (diffusion along grain boundaries)

Factors Affecting Creep and Creep-Resistant Materials

Creep rate increases with higher temperature and higher applied stress. Other factors include grain size (larger grains reduce Coble creep by decreasing grain boundary area) and environmental degradation like oxidation.

Creep-resistant materials are engineered to slow dislocation motion at high temperatures. Nickel-based superalloys, widely used in jet engine turbine blades, are a prime example. Their strengthening strategies include:

• Solid solution strengthening. Alloying elements (Mo, W, Re) distort the lattice and impede dislocation movement.
• Precipitation hardening. Stable precipitates (such as the $\gamma'$ phase in nickel superalloys) act as obstacles to dislocation motion and remain effective at high temperatures.
• Dispersion strengthening. Fine, thermally stable oxide particles (as in oxide dispersion strengthened, or ODS, alloys) pin dislocations and grain boundaries.

Impact Loading and Toughness

Effects of Impact Loading on Materials

Impact loading is the application of a sudden, high-intensity force, producing very high strain rates. Think of a hammer blow, a car crash, or a dropped component. Material behavior under impact differs from behavior under slow (quasi-static) loading in important ways:

• Increased yield strength. At high strain rates, many materials exhibit higher yield and flow stresses because dislocations don't have time to move as easily.
• Reduced ductility. The same rate effect that raises strength tends to reduce the material's ability to deform plastically before fracture.
• Ductile-to-brittle transition. Many BCC metals (including structural steels) undergo a ductile-to-brittle transition as temperature decreases or strain rate increases. The ductile-to-brittle transition temperature (DBTT) is the temperature range where fracture behavior shifts from energy-absorbing ductile tearing to low-energy brittle cleavage. This is critical for structures operating in cold environments (ships, pipelines, bridges).

FCC metals like aluminum and copper generally do not exhibit a sharp DBTT, which is one reason aluminum alloys are used in cryogenic applications.

Toughness and Impact Testing

Toughness is a material's ability to absorb energy and deform plastically without fracturing. It combines both strength and ductility. A material can be strong but brittle (ceramics) or ductile but weak (pure lead); tough materials are both reasonably strong and ductile.

The two standard impact tests are:

• Charpy test. A notched beam specimen is supported at both ends. A pendulum hammer strikes the specimen on the side opposite the notch. The energy absorbed during fracture is measured from the height the pendulum reaches after breaking the specimen.
• Izod test. The specimen is clamped as a vertical cantilever with the notch facing the pendulum strike. It also measures absorbed energy but uses a different specimen geometry and loading configuration.

Both tests produce a single number: absorbed energy in joules (or ft-lbs). By running tests at multiple temperatures, you can plot absorbed energy vs. temperature and identify the DBTT.

For more rigorous analysis, fracture mechanics provides quantitative tools. The stress intensity factor $K$ characterizes the stress field near a crack tip, and the fracture toughness $K_{IC}$ is the critical value at which a crack propagates unstably. The crack tip opening displacement (CTOD) is an alternative measure used especially for materials with significant plasticity at the crack tip. These parameters allow engineers to determine whether an existing crack in a component is safe or will lead to failure under a given load.