Hardness, impact, fatigue and creep testing

Why it matters

Most service failures are not simple overloads: shafts break by fatigue after millions of cycles, boiler tubes and turbine blades fail by creep, and steel structures crack suddenly in cold weather. Hardness checks heat treatment on the shop floor in seconds, impact tests screen steels for brittle fracture, and fatigue and creep data set the life of rotating and high-temperature parts.

Key ideas

Hardness is resistance to localised plastic deformation (indentation). It correlates with tensile strength, so it is the quickest check that a heat treatment worked.

• Brinell (HB / HBW): a hardened steel or tungsten-carbide ball (usually D = 10 mm) pressed with a large load (3000 kgf for steels, 500 kgf for soft metals) for 10–15 s; the indentation diameter d is measured with a microscope. Large indent averages out coarse structures such as cast iron; not for very hard or thin parts.
• Vickers (HV): a square-based diamond pyramid with 136° between opposite faces; the mean diagonal d is measured. One continuous scale from soft to very hard materials; micro-Vickers measures individual phases and case-depth profiles.
• Knoop (HK): an elongated diamond pyramid giving a shallow indent, for thin layers and brittle materials.
• Rockwell (HR): measures depth of penetration under a major load after a minor (preload) load; the number is read directly on a dial. HRC uses a 120° diamond cone with 150 kgf total load (hardened steel); HRB uses a 1/16 in steel ball with 100 kgf (soft steel, brass). Fast and needs no optical measurement, so it suits production checks; it leaves only a small dent.
• Shore scleroscope / rebound: height of rebound of a diamond-tipped hammer; portable, for large parts. For steels, UTS (MPa) ≈ 3.45 × HB is a useful empirical rule.

Impact testing measures the energy absorbed in fracturing a notched specimen at a high strain rate, a measure of notch toughness.

• Charpy: specimen simply supported as a beam, notch facing away from the pendulum, struck at mid-span.
• Izod: specimen held vertically as a cantilever, notch facing the striker.
• Energy absorbed = loss of potential energy of the pendulum = m·g·(h1 − h2).
• Ductile-to-brittle transition (DBTT): BCC metals (ferritic steels) absorb much energy at high temperature (ductile, fibrous fracture) and little at low temperature (brittle cleavage, shiny facets). FCC metals (Al, Cu, austenitic stainless steel) show no transition, which is why they are used for cryogenic service. Fine grain size and low carbon lower the DBTT.

Fatigue is failure under fluctuating stress whose peak is below the yield strength. A crack initiates at a stress raiser (notch, scratch, inclusion, weld toe), grows a little each cycle (leaving beach marks and striations) and finally the remaining section breaks suddenly.

• The S–N (Wöhler) curve plots stress amplitude against cycles to failure on a log scale. Steels and titanium show an endurance limit (about 0.5 × UTS for steels up to UTS ≈ 1400 MPa) below which life is effectively infinite; aluminium and copper alloys do not, so a fatigue strength at 10⁷ or 10⁸ cycles is quoted.
• A tensile mean stress shortens life; the Goodman line corrects for it.
• Improve fatigue life by smooth surfaces, generous fillets, shot peening, carburising or nitriding (all add compressive residual stress at the surface), and by avoiding corrosion (corrosion fatigue removes the endurance limit).

Creep is time-dependent plastic deformation under constant load, significant above about 0.4 of the absolute melting temperature (0.3–0.4 Tm for metals; lead creeps at room temperature).

• Creep curve: instantaneous strain on loading, then primary creep (decreasing rate, strain hardening dominates), secondary or steady-state creep (constant minimum rate, hardening balanced by recovery — the design parameter), and tertiary creep (accelerating rate from necking, voids and grain-boundary cavities) ending in rupture.
• Creep resistance improves with high melting point, coarse grains or single crystals (fewer grain boundaries for sliding), solid-solution and stable precipitate strengthening (nickel superalloys).
• Life at service conditions is extrapolated from short tests at higher temperature using the Larson–Miller parameter.

Formulas

HB = 2F / (π·D·(D − √(D² − d²))) F = load (kgf); D = ball diameter (mm); d = indentation diameter (mm). HB in kgf/mm², quoted as a number. If F is in newtons, multiply by 0.102.

HV = 1.8544·F / d² F = load (kgf); d = mean diagonal (mm).

E_abs = m·g·(h1 − h2) Charpy/Izod energy absorbed (J); m = hammer mass (kg); h1, h2 = heights of the hammer's centre before release and after the swing-through (m).

σm = (σmax + σmin)/2; σa = (σmax − σmin)/2; R = σmin / σmax Mean stress, stress amplitude (Pa) and stress ratio of a fatigue cycle.

σa / Se + σm / Su = 1 Goodman line: Se = endurance limit, Su = ultimate tensile strength (Pa). Combinations on or below the line are safe for infinite life (divide by a factor of safety for design).

σa = σf′·(2Nf)^b Basquin's law for high-cycle fatigue: σf′ = fatigue strength coefficient (Pa), b = fatigue strength exponent (about −0.05 to −0.12), Nf = cycles to failure; both constants come from test data.

ε̇s = A·σⁿ·exp(−Qc / (R·T)) Steady-state creep rate (s⁻¹); A, n (stress exponent) from data; Qc = creep activation energy (J/mol); R = 8.314 J/(mol·K); T in K.

LMP = T·(C + log10 tr) Larson–Miller parameter; T in K, tr = rupture time in hours, C ≈ 20 for steels.

Worked examples

Example 1 (standard): Brinell and Vickers. (a) 10 mm ball, 3000 kgf load, indentation 4.0 mm.

1. √(D² − d²) = √(100 − 16) = 9.165 mm; D − 9.165 = 0.835 mm.
2. HB = 2 × 3000 / (π × 10 × 0.835) = 6000 / 26.23 = 229 HB.
3. Estimated UTS ≈ 3.45 × 229 ≈ 790 MPa. (b) Vickers, 30 kgf, mean diagonal 0.45 mm: HV = 1.8544 × 30 / 0.45² = 275 HV.

Example 2 (standard): Charpy energy. Hammer mass 20 kg falls from h1 = 1.5 m and rises to h2 = 0.9 m after breaking the specimen. E_abs = 20 × 9.81 × (1.5 − 0.9) = 117.7 J.

Example 3 (GATE level): fatigue with mean stress, and creep extrapolation. (a) A steel has Su = 600 MPa and Se = 300 MPa. A part carries σmax = 250 MPa, σmin = −50 MPa. Is it safe for infinite life?

1. σm = (250 − 50)/2 = 100 MPa; σa = (250 + 50)/2 = 150 MPa; R = −0.2.
2. Goodman: σa/Se + σm/Su = 150/300 + 100/600 = 0.5 + 0.167 = 0.667 < 1, so safe (factor of safety 1/0.667 = 1.5). (b) For σf′ = 900 MPa and b = −0.1, the life at σa = 300 MPa (zero mean): 2Nf = (300/900)^(1/−0.1) = 3¹⁰ = 59 049, so Nf ≈ 2.95 × 10⁴ cycles. (c) A steel ruptures in 1000 h at 800 K under a given stress. With C = 20, LMP = 800 × (20 + 3) = 18 400. At 900 K and the same stress: log tr = 18 400/900 − 20 = 0.444, so tr ≈ 2.8 h.

Common mistakes

• Putting F in newtons into the Brinell formula without the 0.102 factor (answers 9.81 times too large).
• Taking Charpy energy as m·g·h1; the absorbed energy is the difference between the initial and final heights.
• Calling hardness tests fully non-destructive; they leave an indentation.
• Confusing stress range (σmax − σmin) with amplitude (half the range).
• Assuming aluminium alloys have an endurance limit.
• Using °C in the Larson–Miller parameter or the Arrhenius creep law.
• Designing on primary creep; the steady-state rate and rupture life are the design inputs.

For GATE PI

Expect one-mark questions on which indenter each hardness test uses, Charpy versus Izod, the ductile-to-brittle transition and which structures show it, the three stages of creep, and factors that improve fatigue life. Numericals cover Brinell/Vickers numbers, pendulum energy, mean and alternating stress with Goodman or Soderberg lines, S–N (Basquin) life, and creep strain from a steady-state rate. Practise unit handling (kgf vs N) and log-scale calculations.

Quick check

1. Which hardness test reads depth of penetration rather than indent size?
2. σmax = 200 MPa and σmin = −200 MPa. What are σm, σa and R?
3. Why is austenitic stainless steel chosen for liquid-nitrogen tanks?
4. A material creeps at a steady 10⁻⁴ per hour. What creep strain accumulates in 1000 h of steady-state creep?
5. Name two treatments that raise the fatigue life of a shaft by putting its surface in compression.

Answers: 1. Rockwell; 2. 0 MPa, 200 MPa, −1; 3. FCC structure, no ductile-to-brittle transition; 4. 0.1 (10 %); 5. Shot peening and carburising (or nitriding, surface rolling).