By the end of this topic, you should be able to...
explain tensile and compressive strength, stiffness, toughness, hardness, malleability, elasticity, plasticity and ductility.
Guiding Question
How do material properties and classifications aid material selection for a specified manufacturing process?
💡 Did You Know? On the night of 14 April 1912, the RMS Titanic's hull steel did not bend around the iceberg — it fractured through it. Metallurgical analysis of recovered hull samples revealed that at 0°C seawater temperature, the steel absorbed only 4–6 joules of impact energy before fracturing. Modern structural ship steel at the same temperature absorbs 200 joules — a forty-fold difference. The Titanic did not sink because of insufficient strength. It sank because of insufficient toughness. These are not the same property — and understanding the difference between toughness, strength, stiffness, hardness, and ductility is precisely what this sub-topic develops.
What Are Mechanical Properties?
Mechanical properties describe the behaviour of materials under applied forces (loads). They quantify how a material responds — deforms, absorbs energy, resists fracture, or yields — when subjected to mechanical stimuli including tension, compression, bending, torsion, impact, and surface indentation.
Understanding mechanical properties is foundational to the material selection process (A3.1.3) because they determine whether a material can safely carry the loads imposed during service without:
Fracturing (catastrophic failure — tensile strength, toughness exceeded)
Deforming excessively (functional failure — stiffness insufficient)
Yielding permanently (dimensional failure — yield strength exceeded)
Wearing or being indented (surface failure — hardness insufficient)
The central analytical tool for understanding mechanical properties of materials is the engineering stress-strain curve — a graphical representation of a material's complete mechanical response from initial loading through to fracture. This curve encodes multiple mechanical properties simultaneously and is developed first as the foundation for all subsequent property explanations.
Engineering Stress
When a force is applied to a material specimen, the engineering stress is defined as the applied force divided by the original cross-sectional area of the undeformed specimen.
SI Unit: Pascal (Pa) = N/m² — for engineering materials, typically expressed in megapascals (MPa) or gigapascals (GPa):
Engineering Strain
When a force is applied, the material deforms. The engineering strain ε\varepsilonε is defined as the change in length divided by the original gauge length.
Tensile Strength
Tensile strength (or Ultimate Tensile Strength — UTS) is the maximum engineering stress a material can withstand before fracture when subjected to a uniaxial tensile (pulling) load. It represents the peak of the stress-strain curve
SI Units: MPa (N/mm²) or GPa
The yield strength is the stress at which permanent (plastic) deformation first occurs — the stress at the yield point. In design, yield strength is the more critical value for ductile materials because yielding produces permanent dimensional change — functional failure — before fracture is reached. A structural component that has yielded permanently may be unacceptable even if it has not fractured.
Compressive Strength
Compressive strength is the maximum stress a material can withstand under a uniaxial compressive (pushing) load before failure. It is measured analogously to tensile strength but with the specimen loaded in compression rather than tension.
Ductile materials in compression undergo barrelling — the material deforms plastically, bulging outward at the equator as the specimen shortens. No fracture occurs (theoretically, a ductile material in pure compression can be deformed indefinitely without fracture — it simply flattens). This is the basis of forging and rolling of metals.
Brittle materials (ceramics, glasses, grey cast iron, concrete) in compression fail by shear fracture along planes inclined at approximately 45°–60° to the loading axis — the internal shear stress on these planes exceeds the material's shear strength before the compressive stress reaches the fracture stress in pure compression. The fracture is sudden, with an audible crack, and produces characteristic angled fracture surfaces.
Stiffness
Stiffness (in the materials science sense) is the resistance of a material to elastic deformation under applied stress — quantified as Young's Modulus
Young's Modulus is defined as the ratio of engineering stress to engineering strain in the linear elastic region of the stress-strain curve.
An important distinction for the designer between structural stiffness vs material stiffness:
Concept | Definition | Symbol | Units | What It Depends On |
Material stiffness (Young's Modulus) | Intrinsic material property — resistance to elastic strain per unit stress | EEE | GPa | Material only — chemical bonding nature and atomic arrangement; independent of geometry |
Structural stiffness | Resistance of a structural member (beam, column, plate) to deflection under load | kkk | N/m | Both material AND geometry — section shape, cross-sectional area, moment of inertia, length |
Toughness
Toughness is the ability of a material to absorb energy and plastically deform before fracturing.
A tough material can absorb large amounts of energy — from impact loads, shock loads, or overloads — without fracturing catastrophically. Toughness is not the same as strength. Toughness is not the same as ductility. It requires both simultaneously.
Material Behaviour | Stress-Strain Character | Toughness | Example |
High strength, low ductility | High stress, low strain before fracture | Low toughness | High-carbon steel wire; glass; ceramics |
Low strength, high ductility | Low stress, large strain before fracture | Moderate toughness | Pure annealed copper, pure aluminium |
High strength AND high ductility | High stress, large strain before fracture | High toughness | Low-alloy structural steel; titanium 6Al-4V; spring steel |
Low strength, low ductility | Low stress, low strain — fracture immediately after elastic limit | Very low toughness (brittle) | Grey cast iron; glass; brick; concrete |
Hardness
Hardness is the resistance of a material to surface indentation, scratching, or permanent deformation at a localised point. It is tested by pressing a rigid indenter (diamond pyramid, steel ball, or diamond cone) into the material surface under a defined load and measuring the size or depth of the resulting indentation.
Units: Hardness is measured on several scales — the choice of scale depends on the material being tested and the magnitude of hardness expected. Hardness is not an SI unit — each scale has its own unit convention.
Surface Hardening — Design Application
For many components (gears, shafts, cams, bearings, tools), the surface must be hard (resist wear, contact stress) while the core must remain tough (resist impact and shock loads without fracture).
Malleability
Malleability is the ability of a material to undergo permanent deformation under compressive stress (hammering, rolling, pressing) without fracturing. A malleable material can be flattened, rolled into sheets, or shaped by compressive working processes without cracking or splitting.
The etymology is directly revealing: from Latin malleus — a hammer. Malleability is the property that was observed by Bronze Age and Iron Age smiths as the defining characteristic that made metals useful for tool and weapon manufacture — the ability to be shaped by hammering.
Malleability vs Ductility—A Critical Distinction
Property | Deformation Mode | Test/Process | Mechanism |
Malleability | Compressive plastic deformation — material spreads laterally under compression | Rolling, forging, pressing, hammering — sheet metal fabrication | Material flows laterally under compressive load; relevant to bulk forming processes |
Ductility | Tensile plastic deformation — material elongates under tension | Wire drawing, tube drawing, deep drawing — tensile forming processes | Material elongates under tensile load; neck forms and specimen fractures when localised plastic instability occurs |
Malleability in Manufacturing — Forming Processes
Malleability directly enables the following primary manufacturing processes:
Process | Material Deformation Mode | Malleability Requirement | Products |
Hot rolling | Steel slab compressed between rotating rolls at 900–1,200°C — progressively reduced in thickness | High malleability at hot-working temperature | Structural steel I-beams, channels, angles, plate, strip |
Cold rolling | Sheet metal compressed between rolls at room temperature | Moderate malleability (strain hardening occurs — material work hardens with each pass; intermediate annealing may be required) | Automotive steel sheet, aluminium foil, copper strip |
Drop forging | Heated billet compressed in shaped die by drop hammer or mechanical press | High malleability at forging temperature | Crankshafts, connecting rods, spanners, axles |
Sheet metal pressing/stamping | Sheet metal deformed into 3D shape in press tool (combination of stretching — ductility, and in-plane flow — malleability) | Requires both malleability and ductility | Automotive body panels, appliance casings |
Embossing / coining | Fine surface detail pressed into sheet metal in a die | High room-temperature malleability and low springback | Coins, medallions, decorative panels |
Spinning | Rotating sheet metal disc worked against a mandrel by roller tool | Good room-temperature malleability | Lampshades, aerospace nosecones, cookware (copper pans) |
Elasticity
Elasticity is the ability of a material to deform under applied stress and return completely to its original dimensions and shape when the stress is removed, with no permanent deformation and no energy loss.
The Elastic Limit — Significance in Design
The elastic limit is the maximum stress a material can withstand while remaining completely elastic. Below the elastic limit, a component will return to its original shape after any load is removed — regardless of how many load cycles are applied. Above the elastic limit, permanent deformation accumulates.
The elastic limit and the yield strength are closely related (the yield strength is the stress at which plastic deformation becomes macroscopically significant and is generally very close to the elastic limit for engineering purposes), but they are formally distinct:
Proportionality limit — stress below which Hooke's Law holds exactly (linear elastic)
Elastic limit — stress below which behaviour is fully elastic (may be slightly above proportionality limit)
Yield strength — stress at which significant plastic deformation begins (slightly above or equal to elastic limit)
For design of components that must not yield (precision machine components, springs, elastic structural elements), the design stress must be maintained below the elastic limit with an appropriate safety factor.
Spring Design
Springs are engineering components designed to operate entirely within the elastic regime — they must undergo large elastic deformation (storing and returning energy elastically) without yielding or fracturing across millions of load cycles.
Ideal spring materials have:
High yield strength — to withstand large stresses without permanent deformation
High elastic limit — to allow large elastic deflections
High Young's modulus — for consistent spring rate (though low modulus materials can be used in elastomeric springs for larger deflections)
High fatigue strength — springs are cyclically loaded
Plasticity
Plasticity is the ability of a material to undergo permanent (irreversible) deformation under applied stress without fracturing. It is the mechanical property that describes the material's behaviour in the plastic region of the stress-strain curve — the region beyond the yield strength where deformation is no longer recoverable.
Plasticity is the enabling property for all metal forming processes — without plasticity, it would be impossible to roll, forge, press, draw, extrude, or bend metals into useful shapes without fracturing them. Plasticity is also the safety mechanism in structural design — a plastically deforming structure absorbs energy and provides visible warning of overload before fracture (unlike a brittle material that fractures without prior deformation).
Ductility
Ductility is a quantitative measure of the degree of plastic deformation a material can undergo before fracturing. Specifically, it quantifies the extent of plastic deformation under tensile loading.
Plasticity vs. Ductility—The Clarification
Property | Broader Definition | Quantification | Key Distinction |
Plasticity | General ability to undergo permanent deformation without fracture — includes both tensile AND compressive deformation | Qualitative property description; not a single number | Encompasses all forms of permanent deformation — more general |
Ductility | Specifically the extent of plastic deformation under tensile loading before fracture | Quantitative: %EL, %RA from tensile test | Specific to tensile deformation; measured by standardised tensile test |
A highly ductile material is necessarily plastic. But plasticity as a term encompasses both ductile (tensile) and malleable (compressive) deformation. In the IB Design Technology curriculum, both plasticity and ductility are listed as distinct properties — plasticity is the general phenomenon; ductility is its tensile-specific quantified expression.
Interconnections Between Properties — The Designer's Map
These properties do not exist independently. Understanding their interdependences is essential for making intelligent material selection decisions (Ashby, 2011).
Property Pair | Relationship |
Strength & Stiffness | Independent — a strong material is not necessarily stiff, and vice versa. A rubber band is neither strong nor stiff. Steel is both strong and stiff. Elastomers are neither. |
Hardness & Toughness | Frequently inversely related. Increasing hardness through heat treatment (quenching) typically reduces ductility and therefore reduces toughness. A glass blade is harder than a steel blade and far less tough. |
Ductility & Tensile Strength | Often inversely related. Alloying, cold working, and heat treatments that increase UTS typically reduce %EL. High-strength steels are less ductile than mild steel. |
Malleability & Ductility | Positively correlated for metals — both are expressions of plasticity. Gold is both highly malleable and highly ductile. Cast iron is neither. |
Elasticity & Plasticity | Sequential and complementary. All materials exhibit elasticity up to their yield point, and then plasticity beyond it. The ratio of elastic to plastic range varies enormously between materials. |
Toughness & Brittleness | Antonyms. A brittle material has minimal plastic region on its stress-strain curve — its toughness is low. Toughness increases as the plastic region broadens. |
The Stress-Strain Curve as a Design Tool
A well-annotated stress-strain curve for a given material communicates the following design-relevant properties simultaneously:
Young's Modulus (E) — gradient of the linear elastic region → stiffness
Yield Strength — stress at transition from elastic to plastic behaviour → onset of permanent deformation
Ultimate Tensile Strength (UTS) — peak stress → maximum load-bearing capacity
Ductility (%EL) — total strain at fracture → wire drawing and forming capacity
Toughness — total area under the curve → energy absorption to fracture
Brittleness — absence of plastic region → low toughness, no warning before fracture
A designer who can read a stress-strain curve can simultaneously answer the questions: Will it deflect excessively? Will it yield under design loads? How much energy will it absorb in a crash? Will it fail without warning? — from a single graph.
Key Vocabulary
Master these definitions precisely. The IB examiner will award marks for correct use of technical terminology. Vague answers using everyday language — "strong," "hard," "flexible" — will not score at the highest levels.
Term | Precise Definition |
Stress (σ) | The internal force per unit cross-sectional area within a material, generated in response to an applied external load. Measured in megapascals (MPa) or gigapascals (GPa). (Callister & Rethwisch, 2018) |
Strain (ε) | The fractional change in dimension of a material in response to applied stress — a dimensionless ratio of deformation to original dimension. (Callister & Rethwisch, 2018) |
Young's Modulus (E) | The ratio of stress to strain in the elastic region of deformation — a material constant defining its intrinsic stiffness, independent of geometry. Measured in GPa. (Ashby, 2011) |
Elastic limit | The maximum stress below which a material will deform elastically — returning to its original dimensions when the load is removed. Beyond this point, permanent deformation occurs. (Callister & Rethwisch, 2018) |
Yield point / Yield strength | The stress at which a material transitions from elastic to plastic deformation — the onset of permanent, unrecoverable dimensional change. (Callister & Rethwisch, 2018) |
Tensile strength | The maximum stress a material can sustain when subjected to a uniaxial tensile (pulling) load before fracture or uncontrolled plastic deformation. Also termed Ultimate Tensile Strength (UTS). (Ashby & Jones, 2012) |
Compressive strength | The maximum stress a material can sustain when subjected to a compressive (pushing) load before fracture or structural failure. (Callister & Rethwisch, 2018) |
Stiffness | The resistance of a material or structure to elastic deformation per unit load — characterised at the material level by Young's Modulus. A stiff material deforms very little under load and returns fully to its original shape. (Ashby, 2011) |
Toughness | The ability of a material to absorb mechanical energy and deform plastically without fracturing — quantified as the total area under the stress-strain curve. A tough material combines adequate strength with adequate ductility. (Callister & Rethwisch, 2018) |
Hardness | The resistance of a material's surface to permanent indentation, scratching, or localised plastic deformation. Measured on Vickers (HV), Brinell (HB), or Rockwell (HR) scales. (Ashby & Jones, 2012) |
Malleability | The ability of a material to undergo extensive plastic deformation under compressive stress — to be permanently shaped by hammering, rolling, or pressing — without fracturing. (Callister & Rethwisch, 2018) |
Elasticity | The ability of a material to deform under load and return completely to its original shape and dimensions when the load is removed — the material stores and releases elastic strain energy. (Ashby, 2011) |
Plasticity | The ability of a material to undergo permanent, irreversible deformation beyond the yield point without fracturing — the material does not return to its original shape when the load is removed. (Callister & Rethwisch, 2018) |
Ductility | The ability of a material to undergo extensive plastic deformation under tensile stress — to be drawn into wires or stretched — without fracturing. |
Fracture | The separation of a material under stress — either brittle fracture (with minimal plastic deformation, no warning) or ductile fracture (preceded by significant plastic deformation and necking). (Callister & Rethwisch, 2018) |
Stress-strain curve | A graphical representation of a material's mechanical response — plotting stress (σ) on the vertical axis against strain (ε) on the horizontal axis — from which all primary mechanical properties can be determined. (Ashby, 2011) |
Practice Questions
Question 1 — Command Term: State
State one difference between tensile strength and compressive strength.
What this requires: A single, concise, accurate statement contrasting the two properties — the direction of loading or the magnitude relationship for brittle materials.
Question 2 — Command Term: State
State the unit in which Young's Modulus is measured and identify what region of the stress-strain curve it is derived from.
What this requires: Unit (GPa or Pa) and identification of the linear elastic region.
Question 3 — Command Term: Describe
Describe the difference between elastic and plastic deformation, with reference to what occurs at the atomic level in a metallic material.
What this requires: Description of bond stretching and recovery (elastic) versus dislocation movement and permanent atomic displacement (plastic). Reference to the yield point as the boundary between the two regimes.
Question 4 — Command Term: Describe
Describe how toughness is represented on a stress-strain curve and explain why a highly hard material may have low toughness.
What this requires: Description of toughness as total area under the curve; explanation that hardening treatments reduce the plastic region (ductility), reducing area under the curve, even if peak stress (UTS) increases.
Question 5 — Command Term: Explain
Explain why engineers designing crash structures for automotive applications specify materials with high toughness rather than maximum hardness.
What this requires: Definition of toughness as energy absorption to fracture; explanation of crash structure function as kinetic energy absorption; contrast with hardness as surface resistance to indentation — irrelevant to bulk energy absorption. Link to plastic deformation as the energy absorption mechanism.
Question 6 — Command Term: Explain
Explain why concrete is used for structural columns but requires steel reinforcement in beams. Reference the relevant mechanical properties in your answer.
What this requires: Explanation of the difference between compressive strength and tensile strength; concrete's high compressive strength but near-zero tensile strength; columns loaded in compression (concrete effective), beams loaded in bending with tension in the lower fibre (concrete inadequate without reinforcement); steel's high tensile strength filling the deficit.
Question 7 — Command Term: Compare
Compare the mechanical behaviour of a ductile metal such as mild steel and a brittle material such as grey cast iron under tensile loading, with reference to their stress-strain curves.
What this requires: Direct comparison — elastic behaviour of both; yield point and plastic region of mild steel versus absence of plastic region in cast iron; ductility and toughness of mild steel versus low ductility and toughness of cast iron; warning of failure versus sudden brittle fracture. Reference to fracture surface characteristics a bonus.
Question 8 — Command Term: Evaluate
Evaluate the statement: "A high Young's Modulus is always desirable in a structural material." Use named material examples to support your argument.
What this requires: The highest-demand command term. Acknowledge contexts where high stiffness is critical — structural frames, precision engineering. Present counter-arguments: applications requiring compliance — springs, shock absorption, seals, biomedical implants (bone's modulus match), flexible electronics. Identify the stiffness-toughness trade-off. Reach a nuanced, justified conclusion that the desired stiffness is determined entirely by the loading context, not by any universal hierarchy of desirability.
Sources
Ashby, M.F. (2011). Materials Selection in Mechanical Design. 4th edn. Butterworth-Heinemann, Oxford.
Ashby, M.F. and Jones, D.R.H. (2012). Engineering Materials 1: An Introduction to Properties, Applications and Design. 4th edn. Butterworth-Heinemann, Oxford.
Callister, W.D. and Rethwisch, D.G. (2018). Materials Science and Engineering: An Introduction. 10th edn. Wiley, New York.
International Baccalaureate Organization (2024). Design Technology Guide: Diploma Programme. First Assessment 2027. IBO, Geneva.
Linking Questions
Why is a good understanding of material properties important when designing structural systems? (A3.2)
When do the physical properties of materials restrict the ability to use certain prototyping techniques? (A2.2)
How do the properties of a material influence the choice of manufacturing techniques for a product? (A4.1)
How can the characteristics of a material limit the effectiveness of modelling and prototyping as designs are developed? (B2.2)
How important is an understanding of the mechanical properties of a material when considering structural and mechanical systems, and their applications? (A3.2, A3.3, B3.2, B3.3)
Which classifications of properties are important when developing electronic systems and their applications? (A3.4, B3.4)
How could the continued development of biodegradable materials influence designers’ ability to address aspects of design for sustainability and design for a circular economy? (C2.1, C2.2)
Why is a thorough understanding of materials key for effective product analysis and evaluation of products? (C3.1)
How do design decisions related to the properties of materials and components impact a product’s life-cycle analysis? (C3.2)