Materials Science · Cracks, fracture and toughness

Brittle and ductile fracture mechanisms

Follow the processes that turn local separation into fracture. Compare cleavage, void nucleation and coalescence, then use deformation, work and temperature evidence without giving a material a permanent brittle or ductile label.

Useful background: Elasticity, plasticity and tensile strength. Each worked case explains the quantities it uses.

Back to the chapter

After reading, you can

Explain cleavage and a common ductile void-growth/coalescence sequence at the crack scale.
Distinguish fracture mechanism, crack path and macroscopic deformation, including mixed observations.
Explain why temperature, rate, constraint and microstructure can change which process dominates.
Calculate work from a simple force–displacement path and interpret a stated transition criterion with appropriate limits.

Different mechanisms consume energy

Imagine two matched test pieces reaching the same maximum force. One breaks after little permanent change of shape. The other stretches and narrows substantially before separating. The force maximum alone does not tell us what happened near the crack. We need the deformation history and the physical process that created the fracture surfaces.

Brittle fracture advances with limited plastic accommodation relative to the separation process. Ductile fracture involves substantial plastic deformation, which can be concentrated in a small zone rather than obvious throughout the whole specimen. These descriptions concern the observed response under specified conditions. A brittle-looking specimen need not have had literally zero local slip, and a material called a metal is not guaranteed to fracture ductilely.

Plastic flow and cracking interact. Slip can change the crack-tip shape and redistribute stress, consuming work before the crack advances. Plastic deformation can also nucleate and grow damage that eventually joins into a crack. Calling plasticity beneficial without asking where and how it occurs therefore misses part of the mechanism.

Cleavage is a mechanism; a grain boundary is a path

In a crystalline solid, cleavage separates material along a crystallographic plane by breaking bonds across it. A grain is a region with a particular crystal orientation. A cleavage crack can cut through grains and change direction as it meets differently oriented regions. Its facets can therefore reflect the crystal structure. Slip and cleavage are distinct processes: one changes shape by dislocation motion, while the other creates separation. Their competition depends on the material and local state.

A crack can instead separate along interfaces between grains. That is an intergranular path; a path through grain interiors is transgranular. These words describe where the crack goes, not by themselves how much plastic deformation occurred. Boundary weakening can favor brittle separation, but voids located at boundary particles can also join along a boundary in a ductile process. Do not turn path names into a brittle-versus-ductile test.

Cleavage is not the name for every brittle fracture. Glass lacks a long-range crystal lattice, so it cannot have crystallographic cleavage planes, yet it can fracture with little macroscopic plasticity. Nor does a smooth or rough surface alone identify a unique mechanism. Interpret its features at an appropriate scale with the specimen’s loading and material history.

A common ductile route: make cavities, enlarge them, join them

Consider a relatively hard inclusion or second-phase particle inside a deforming metal matrix. Matrix means the surrounding material. If the particle and matrix deform differently, local stresses can build around the particle. A cavity, also called a void, can start when the particle cracks or when its interface separates from the matrix. This is void nucleation: a new cavity appears. It is different from making an existing cavity bigger.

Continued plastic deformation can enlarge a cavity. The amount and direction of tensile stress matter as well as accumulated strain. A tensile stress state that pulls in several directions can favor cavity growth; a simple statement that all local stresses stop at the uniaxial yield value misses that stress-state dependence. The surrounding metal must deform as the void grows.

Eventually neighboring cavities interact. The metal ligament between them can thin and fail, or deformation can localize into a shear band linking them. Their joining is coalescence. A connected crack can then advance by repeating damage in material ahead of it. Nucleation, growth and coalescence can overlap in time across different particles, rather than occur everywhere as three perfectly separate stages.

A dimpled fracture surface often records such cavities; an initiating particle may remain inside a dimple. This makes dimples useful evidence, not a direct numerical toughness meter. Void coalescence is common in ductile metals, but other ductile routes include strong necking and localized shear. The schematic shows one route and is not an image of every alloy.

Four conceptual frames show particles in a matrix, new cavities at interfaces, larger cavities with a narrower metal ligament, and one joined opening after ligament failure. Purple dots are particles; orange outlines are void boundaries. The sequence has no claimed spatial scale or measured timing.

A transition depends on competing processes and conditions

For some steels, cooling makes plastic accommodation more difficult under the imposed loading while cleavage can still occur. The local tensile loading can then drive separation before extensive plastic deformation develops. Raising the loading rate can also make plastic accommodation harder in susceptible materials. This is a competition between processes, not proof that the composition changed between tests. It does not imply that every metal has the same transition, or any sharp transition at all.

Microstructure changes the competition. For example, an effective grain structure that interrupts cleavage can make long crack advance harder. Particle population and interfaces influence ductile damage. Constraint, meaning restriction of local deformation by surrounding material, changes the stress state and can favor different damage or separation routes. Temperature, rate, constraint and microstructure therefore belong with a fracture observation. The next geometry lesson explains how thickness can change constraint.

A measured impact-energy versus temperature curve can summarize a transition for a specified specimen and rate. It may show lower and upper shelves with a steep region between them. A reported transition temperature needs a criterion, such as a chosen absorbed energy or a chosen fracture-appearance measure. Different criteria can give different temperatures on the same data. Scatter and the actual specimen temperature also matter, especially where the curve is steep.

Invented matched impact tests for an interpolation exercise. These are not measurements of a named steel.
Temperature (°C)	Absorbed energy (J)
−80	12
−40	24
0	64
40	95

Combine observations instead of diagnosing from one clue

Start with the loading record and the permanent shape change. Then ask where the crack started and what microscopic features appear along its path. Dimples support a void-growth/coalescence explanation; cleavage-related facets support a crystalline separation explanation. A single fracture can contain both. Their distribution can change from the free surface to a constrained interior, or as the crack advances.

Total work from a force–specimen-displacement trace is the area beneath that path: W ≈ Σ[(F_i + F_(i+1))/2]Δδ_i for straight segments between measured points. Here Δδ_i is the displacement increment from point i to point i + 1. Each trapezoid is average force times that additional displacement. If force is in kN and displacement in mm, 1 kN·mm = 1 J. Matching maximum forces need not give matching areas.

The area does not isolate bond-breaking energy or determine a unique microscopic route. It can include stored elastic energy, plastic deformation and damage; a real dynamic measurement has additional measurement issues. To connect the area with a mechanism, use independent observations such as permanent deformation and microscopy. To determine a fracture-mechanics resistance, use the appropriate defined crack test rather than relabel this work as K_IC.

Both invented paths peak at 10 kN at 0.20 mm. Solid A falls to zero by 0.25 mm and has work 1.25 J. Dashed B holds 10 kN to 1.00 mm, falls to zero at 1.50 mm and has work 11.50 J. Both axes start at zero; points define straight segments.

Worked examples

Same peak force, different work and observations

Two invented matched specimens have straight force–specimen-displacement segments through these points, written as (mm, kN): A: (0,0), (0.20,10), (0.25,0); B: (0,0), (0.20,10), (1.00,10), (1.50,0). Find their work. What can be inferred if separate observations show little permanent deformation and cleavage-related facets for A, but necking and dimples for B?

For A, the rising triangle contributes ½ × 10 × 0.20 = 1.00 J. The descending triangle adds ½ × 10 × 0.05 = 0.25 J. Total W_A = 1.25 J.
For B, the same initial triangle contributes 1.00 J. The plateau contributes 10 × (1.00 − 0.20) = 8.00 J. The final triangle contributes ½ × 10 × 0.50 = 2.50 J. Total W_B = 11.50 J.
Both peaks are 10 kN, but B takes 11.50/1.25 = 9.2 times the loading work in these prescribed tests. The additional displacement matters.
The separately supplied permanent-shape and surface observations support limited-plasticity cleavage for A and ductile void rupture for B. The curves alone would not establish those microscopic mechanisms.
Do not infer a 9.2-fold K_IC ratio, an intrinsic property ratio or an equal fraction of work spent creating surfaces. Those quantities have not been measured.

A takes 1.25 J and B 11.50 J. Combined observations support different dominant mechanisms; matching peak force does not imply matching work or fracture resistance.

Estimate a temperature for a deliberately chosen criterion

For the invented impact table, choose 50 J as a teaching criterion and use straight-line interpolation between neighboring points. At what temperature is it reached? Is that a universal transition temperature?

50 J lies between 24 J at −40 °C and 64 J at 0 °C, so use that interval rather than either shelf.
The fraction of the energy rise is (50 − 24)/(64 − 24) = 26/40 = 0.65.
Take the same fraction of the 40 °C interval: T = −40 + 0.65 × 40 = −14 °C. The local straight-line slope is 1 J/°C.
This reports the temperature for the chosen 50 J criterion on the supplied illustrative curve. The 50 J choice is not a test-standard requirement. Another criterion, rate, notch, orientation or material condition can change the reported result.

About −14 °C for this chosen criterion and interpolation. It is not a universal material constant or an acceptance threshold.

Separate the crack path from the mechanism

A hypothetical microscopy report says the crack follows grain boundaries and shows cavities joined around boundary particles. The bulk specimen also retains substantial permanent deformation. A summary labels the fracture brittle solely because it is intergranular. Is that justified?

Intergranular describes the path along grain boundaries. It does not specify how that path formed.
Cavities around particles and their joining are consistent with a void mechanism. Permanent deformation supplies complementary evidence for plastic flow.
The supplied observations support intergranular ductile damage as a plausible explanation. Look for mixed regions and the actual test history before assigning a dominant mechanism.
A numerical resistance still requires its defined measurement; the path description and microscopy do not supply it.

No. Boundary-following fracture can involve ductile void growth and coalescence; the path label alone cannot settle the mechanism.

Try the reasoning

A crystalline specimen breaks with little visible bending. A local measurement nevertheless detects slip near the crack tip. Does the slip automatically contradict a predominantly brittle fracture description?
Show the answer and reasoning
No. A limited local plastic process can coexist with separation that occurs before extensive plastic accommodation.
Macroscopic shape, local slip and the dominant crack mechanism refer to different scales. Quantify deformation and examine the crack path; do not equate brittle with absolutely no atomic rearrangement or slip.
Two particles nucleate cavities at the same strain in two hypothetical microstructures. The initial inter-particle ligament is shorter in the second. If cavity growth paths were otherwise comparable, why might joining occur after less additional extension there?
Show the answer and reasoning
The cavities need less growth to eliminate the shorter connecting ligament.
This is a conditional geometric argument for coalescence, not a claim that spacing alone predicts fracture. Particle size, interface behavior, stress state and localization can also differ.
A new invented path has points (0 mm,0 kN), (0.5 mm,8 kN), (1.0 mm,0 kN). Calculate work. Can its peak of 8 kN be used to conclude that it took less work than specimen A in the worked example?
Show the answer and reasoning
The work is 4 J, which exceeds A’s 1.25 J despite the smaller peak.
The two triangle areas are each ½ × 8 × 0.5 = 2 J. A lower force acting through greater displacement can do more work. No microscopic mechanism is identified by this calculation alone.
Use the impact table to estimate the temperature for a different chosen criterion of 75 J. What does the difference from −14 °C teach?
Show the answer and reasoning
About 14.2 °C, using the interval from 0 °C,64 J to 40 °C,95 J.
The fraction is (75 − 64)/(95 − 64) = 11/31, giving T = 40 × 11/31 ≈ 14.2 °C. Different stated criteria give different temperatures on the same curve, so report the criterion with the value.
A specimen has dimples near an outer surface and cleavage-related facets in an interior region. Propose an interpretation and an observation that would test it.
Show the answer and reasoning
A mixed fracture is plausible, with a change in local constraint or mechanism across the specimen. Compare mapped surface features with local deformation and geometry.
A free surface and constrained interior need not have the same state. The features motivate a hypothesis; the actual location of initiation, loading history and microscopic evidence are needed before assigning a cause. A single adjective for the entire surface loses useful information.

What to carry forward

Explain the process: cleavage separates on crystal planes; a common ductile route nucleates, grows and joins cavities.
Intergranular and transgranular describe crack paths, not a complete brittle/ductile classification.
Temperature, rate, microstructure and constraint can change competing processes without a composition change.
Combine work, permanent deformation and microscopic evidence; neither a peak force nor a surface clue supplies K_IC.

References

Teaching resources and research supporting this lesson’s explanations and examples.