Impact Test

Materials Science · FE Reference Handbook section

Materials Science

0 formulas

10 exam-style examples

~45 min

All Materials Science lectures

Handbook notes for this section

Definitions and conditions exactly as the handbook states them.

The Charpy Impact Test is used to find energy required to fracture and to identify ductile to brittle transition.
Impact tests determine the amount of energy required to cause failure in standardized test samples. The tests are repeated over a
range of temperatures to determine the ductile to brittle transition temperature.

Core formulas for this FE topic

Definitions, applicability, units, assumptions and worked examples for each relation.

This section is conceptual; there are no equations to memorise.

Worked exam-style examples

The four ways this section is written on the real exam — thoughts first, then equations, then substitution.

Example 1

Hardness-to-strength conversion and ASTM grain size — Impact Test

A steel component measures 287 BHN. Estimate its tensile strength from the hardness relationship, then determine how many grains per square inch at 100× correspond to an ASTM grain size number of 6.

Given

$BHN = 287$
$ASTM grain size n = 6$

Find

Approximate tensile strength and grains per in² at 100×

Start with the thinking

For steels the empirical relation between hardness and tensile strength is TS ≈ 500 × BHN in psi.
The ASTM grain size number doubles the grain count for every increment of one.

Step-by-step solution

Formula — TS (psi) ≈ 500 × BHN
Substituting
$TS = 500 \times 287 = 143,500 psi = 143.5 ksi$
Formula
$N = 2^(n-1) grains per in^{2} at 100\times$
Substituting
$N = 2^(6 - 1) = 32 grains/in^{2}$
Interpretation — finer grains (higher n) raise yield strength through the Hall-Petch effect

Answer:

TS \approx 143.5 ksi; N = 32 grains/in^{2}

Why the other options are there

0.57 ksi (ratio inverted)
64 grains/in² (exponent off by one)

Reference: FE Reference Handbook — Materials Science → Impact Test

Example 2

Hardness-to-strength conversion and ASTM grain size — Impact Test (2)

A steel component measures 311 BHN. Estimate its tensile strength from the hardness relationship, then determine how many grains per square inch at 100× correspond to an ASTM grain size number of 9.

Given

$BHN = 311$
$ASTM grain size n = 9$

Find

Approximate tensile strength and grains per in² at 100×

Start with the thinking

For steels the empirical relation between hardness and tensile strength is TS ≈ 500 × BHN in psi.
The ASTM grain size number doubles the grain count for every increment of one.

Step-by-step solution

Formula — TS (psi) ≈ 500 × BHN
Substituting
$TS = 500 \times 311 = 155,500 psi = 155.5 ksi$
Formula
$N = 2^(n-1) grains per in^{2} at 100\times$
Substituting
$N = 2^(9 - 1) = 256 grains/in^{2}$
Interpretation — finer grains (higher n) raise yield strength through the Hall-Petch effect

Answer:

TS \approx 155.5 ksi; N = 256 grains/in^{2}

Why the other options are there

0.62 ksi (ratio inverted)
512 grains/in² (exponent off by one)

Reference: FE Reference Handbook — Materials Science → Impact Test

Example 3

Hardness-to-strength conversion and ASTM grain size — Impact Test (3)

A steel component measures 174 BHN. Estimate its tensile strength from the hardness relationship, then determine how many grains per square inch at 100× correspond to an ASTM grain size number of 5.

Given

$BHN = 174$
$ASTM grain size n = 5$

Find

Approximate tensile strength and grains per in² at 100×

Start with the thinking

For steels the empirical relation between hardness and tensile strength is TS ≈ 500 × BHN in psi.
The ASTM grain size number doubles the grain count for every increment of one.

Step-by-step solution

Formula — TS (psi) ≈ 500 × BHN
Substituting
$TS = 500 \times 174 = 87,000 psi = 87.0 ksi$
Formula
$N = 2^(n-1) grains per in^{2} at 100\times$
Substituting
$N = 2^(5 - 1) = 16 grains/in^{2}$
Interpretation — finer grains (higher n) raise yield strength through the Hall-Petch effect

Answer:

TS \approx 87 ksi; N = 16 grains/in^{2}

Why the other options are there

0.35 ksi (ratio inverted)
32 grains/in² (exponent off by one)

Reference: FE Reference Handbook — Materials Science → Impact Test

Example 4

Hardness-to-strength conversion and ASTM grain size — Impact Test (4)

A steel component measures 331 BHN. Estimate its tensile strength from the hardness relationship, then determine how many grains per square inch at 100× correspond to an ASTM grain size number of 4.

Given

$BHN = 331$
$ASTM grain size n = 4$

Find

Approximate tensile strength and grains per in² at 100×

Start with the thinking

For steels the empirical relation between hardness and tensile strength is TS ≈ 500 × BHN in psi.
The ASTM grain size number doubles the grain count for every increment of one.

Step-by-step solution

Formula — TS (psi) ≈ 500 × BHN
Substituting
$TS = 500 \times 331 = 165,500 psi = 165.5 ksi$
Formula
$N = 2^(n-1) grains per in^{2} at 100\times$
Substituting
$N = 2^(4 - 1) = 8 grains/in^{2}$
Interpretation — finer grains (higher n) raise yield strength through the Hall-Petch effect

Answer:

TS \approx 165.5 ksi; N = 8 grains/in^{2}

Why the other options are there

0.66 ksi (ratio inverted)
16 grains/in² (exponent off by one)

Reference: FE Reference Handbook — Materials Science → Impact Test

Example 5

Hardness-to-strength conversion and ASTM grain size — Impact Test (5)

A steel component measures 289 BHN. Estimate its tensile strength from the hardness relationship, then determine how many grains per square inch at 100× correspond to an ASTM grain size number of 6.

Given

$BHN = 289$
$ASTM grain size n = 6$

Find

Approximate tensile strength and grains per in² at 100×

Start with the thinking

For steels the empirical relation between hardness and tensile strength is TS ≈ 500 × BHN in psi.
The ASTM grain size number doubles the grain count for every increment of one.

Step-by-step solution

Formula — TS (psi) ≈ 500 × BHN
Substituting
$TS = 500 \times 289 = 144,500 psi = 144.5 ksi$
Formula
$N = 2^(n-1) grains per in^{2} at 100\times$
Substituting
$N = 2^(6 - 1) = 32 grains/in^{2}$
Interpretation — finer grains (higher n) raise yield strength through the Hall-Petch effect

Answer:

TS \approx 144.5 ksi; N = 32 grains/in^{2}

Why the other options are there

0.58 ksi (ratio inverted)
64 grains/in² (exponent off by one)

Reference: FE Reference Handbook — Materials Science → Impact Test

Example 6

Hardness-to-strength conversion and ASTM grain size — Impact Test (6)

A steel component measures 188 BHN. Estimate its tensile strength from the hardness relationship, then determine how many grains per square inch at 100× correspond to an ASTM grain size number of 4.

Given

$BHN = 188$
$ASTM grain size n = 4$

Find

Approximate tensile strength and grains per in² at 100×

Start with the thinking

For steels the empirical relation between hardness and tensile strength is TS ≈ 500 × BHN in psi.
The ASTM grain size number doubles the grain count for every increment of one.

Step-by-step solution

Formula — TS (psi) ≈ 500 × BHN
Substituting
$TS = 500 \times 188 = 94,000 psi = 94.0 ksi$
Formula
$N = 2^(n-1) grains per in^{2} at 100\times$
Substituting
$N = 2^(4 - 1) = 8 grains/in^{2}$
Interpretation — finer grains (higher n) raise yield strength through the Hall-Petch effect

Answer:

TS \approx 94 ksi; N = 8 grains/in^{2}

Why the other options are there

0.38 ksi (ratio inverted)
16 grains/in² (exponent off by one)

Reference: FE Reference Handbook — Materials Science → Impact Test

Example 7

Hardness-to-strength conversion and ASTM grain size — Impact Test (7)

A steel component measures 152 BHN. Estimate its tensile strength from the hardness relationship, then determine how many grains per square inch at 100× correspond to an ASTM grain size number of 6.

Given

$BHN = 152$
$ASTM grain size n = 6$

Find

Approximate tensile strength and grains per in² at 100×

Start with the thinking

For steels the empirical relation between hardness and tensile strength is TS ≈ 500 × BHN in psi.
The ASTM grain size number doubles the grain count for every increment of one.

Step-by-step solution

Formula — TS (psi) ≈ 500 × BHN
Substituting
$TS = 500 \times 152 = 76,000 psi = 76.0 ksi$
Formula
$N = 2^(n-1) grains per in^{2} at 100\times$
Substituting
$N = 2^(6 - 1) = 32 grains/in^{2}$
Interpretation — finer grains (higher n) raise yield strength through the Hall-Petch effect

Answer:

TS \approx 76 ksi; N = 32 grains/in^{2}

Why the other options are there

0.30 ksi (ratio inverted)
64 grains/in² (exponent off by one)

Reference: FE Reference Handbook — Materials Science → Impact Test

Example 8

Hardness-to-strength conversion and ASTM grain size — Impact Test (8)

A steel component measures 191 BHN. Estimate its tensile strength from the hardness relationship, then determine how many grains per square inch at 100× correspond to an ASTM grain size number of 8.

Given

$BHN = 191$
$ASTM grain size n = 8$

Find

Approximate tensile strength and grains per in² at 100×

Start with the thinking

For steels the empirical relation between hardness and tensile strength is TS ≈ 500 × BHN in psi.
The ASTM grain size number doubles the grain count for every increment of one.

Step-by-step solution

Formula — TS (psi) ≈ 500 × BHN
Substituting
$TS = 500 \times 191 = 95,500 psi = 95.5 ksi$
Formula
$N = 2^(n-1) grains per in^{2} at 100\times$
Substituting
$N = 2^(8 - 1) = 128 grains/in^{2}$
Interpretation — finer grains (higher n) raise yield strength through the Hall-Petch effect

Answer:

TS \approx 96 ksi; N = 128 grains/in^{2}

Why the other options are there

0.38 ksi (ratio inverted)
256 grains/in² (exponent off by one)

Reference: FE Reference Handbook — Materials Science → Impact Test

Example 9

Hardness-to-strength conversion and ASTM grain size — Impact Test (9)

A steel component measures 158 BHN. Estimate its tensile strength from the hardness relationship, then determine how many grains per square inch at 100× correspond to an ASTM grain size number of 6.

Given

$BHN = 158$
$ASTM grain size n = 6$

Find

Approximate tensile strength and grains per in² at 100×

Start with the thinking

For steels the empirical relation between hardness and tensile strength is TS ≈ 500 × BHN in psi.
The ASTM grain size number doubles the grain count for every increment of one.

Step-by-step solution

Formula — TS (psi) ≈ 500 × BHN
Substituting
$TS = 500 \times 158 = 79,000 psi = 79.0 ksi$
Formula
$N = 2^(n-1) grains per in^{2} at 100\times$
Substituting
$N = 2^(6 - 1) = 32 grains/in^{2}$
Interpretation — finer grains (higher n) raise yield strength through the Hall-Petch effect

Answer:

TS \approx 79 ksi; N = 32 grains/in^{2}

Why the other options are there

0.32 ksi (ratio inverted)
64 grains/in² (exponent off by one)

Reference: FE Reference Handbook — Materials Science → Impact Test

Example 10

Hardness-to-strength conversion and ASTM grain size — Impact Test (10)

A steel component measures 206 BHN. Estimate its tensile strength from the hardness relationship, then determine how many grains per square inch at 100× correspond to an ASTM grain size number of 8.

Given

$BHN = 206$
$ASTM grain size n = 8$

Find

Approximate tensile strength and grains per in² at 100×

Start with the thinking

For steels the empirical relation between hardness and tensile strength is TS ≈ 500 × BHN in psi.
The ASTM grain size number doubles the grain count for every increment of one.

Step-by-step solution

Formula — TS (psi) ≈ 500 × BHN
Substituting
$TS = 500 \times 206 = 103,000 psi = 103.0 ksi$
Formula
$N = 2^(n-1) grains per in^{2} at 100\times$
Substituting
$N = 2^(8 - 1) = 128 grains/in^{2}$
Interpretation — finer grains (higher n) raise yield strength through the Hall-Petch effect

Answer:

TS \approx 103.0 ksi; N = 128 grains/in^{2}

Why the other options are there

0.41 ksi (ratio inverted)
256 grains/in² (exponent off by one)

Reference: FE Reference Handbook — Materials Science → Impact Test