Fracture toughness testing (KIc): test, formula, standards and values

Fracture toughness (K_Ic) is a material's resistance to the unstable propagation of an existing crack. It is the critical value of the stress intensity factor K = Yσ√(πa), in MPa√m. A fracture toughness test to ASTM E399 measures it on a fatigue pre-cracked test specimen, loaded while a clip gauge records the crack opening.

Do not confuse it with toughness, which is the energy absorbed up to fracture (J/m³ in the tensile test, or joules in the Charpy test). Fracture toughness answers a different question: given a crack of known size, what stress can the part carry before the crack runs? This guide covers the definition, the formula and the units (MPa√m and ksi√in), the effect of thickness, fracture toughness testing step by step with the calculation of K_Q and the validity criteria, the choice between K_Ic, the J-integral and CTOD, the standards (editions checked on October 13, 2026), typical values with sources, four worked examples and the most common mistakes.

What is fracture toughness

Fracture toughness is the property that measures how strongly a material resists the growth of a sharp crack that is already present, expressed as the value of K at the crack tip at the moment the crack starts to grow unstably. Every real part has defects: casting pores, inclusions, weld flaws, fatigue cracks that started in service. The design question is no longer "what stress can the material carry" but "what stress can the material carry with this defect". That is the question fracture toughness answers.

The theory rests on two milestones. Griffith (Philosophical Transactions of the Royal Society A, 1921) showed, through an energy balance, that the strength of brittle solids such as glass is governed by microscopic cracks, not by the cohesion between atoms. Irwin (Journal of Applied Mechanics, 1957) described the stress field at a crack tip with a single parameter, the stress intensity factor K, which combines the applied stress, the crack size and the geometry. This is linear elastic fracture mechanics (LEFM): it holds as long as the plastic zone at the crack tip is small compared with the crack and the part.

The subscript of K_Ic has two meanings: the "I" refers to loading mode I, explained below, and the "c" means critical. In other texts the same symbol appears as KIC, K1c or K1C. ASTM E399, in the official summary of its scope, describes K_Ic as a probable lower limit of the material's toughness, measured with minimal plasticity at the crack tip.

Loading modes I, II and III

A crack can be loaded in three ways, and each has its own stress intensity factor (K_I, K_II and K_III). The diagram below shows the three modes on a block with a crack entering from the front face: in mode I, the forces are normal to the crack plane and open the faces; in mode II, the faces slide over each other in the direction perpendicular to the crack front; in mode III, they slide in the direction parallel to the front, as when tearing a sheet of paper.

Mode I is the most severe in most materials and is the only one standardized by the test standards: ASTM E1820 defines its scope as fracture in the opening mode (mode I). In practice, a crack under mixed-mode loading tends to change direction until it is perpendicular to the largest tensile stress, that is, until it works in mode I. That is why, when fracture toughness is mentioned without qualification, it means K_Ic.

Is fracture toughness a material property?

A valid K_Ic is indeed a material property: measured under plane strain, it does not depend on the shape or size of the test specimen, and the value obtained in one laboratory applies to a part of the same material, heat treatment and orientation. By contrast, the toughness measured in thin sheet (K_C), and J and CTOD values obtained on specimens without enough constraint, depend on thickness and geometry (NDE-ED, Iowa State University). The section on thickness, further on, shows why.

Even a valid K_Ic depends on conditions that must be reported with the result: temperature, loading rate and the orientation of the crack relative to the rolling or forging direction. A 7075 alloy tested with the crack running along the rolling direction gives a different number from the same 7075 with the crack in the transverse direction.

Toughness and fracture toughness: what is the difference

Toughness is energy; fracture toughness is resistance to crack growth. Toughness is the energy the material absorbs up to fracture: in the tensile test, it is the area under the stress-strain curve, in J/m³; in the Charpy test, it is the energy the pendulum spends to break a V-notched test specimen, in joules. Fracture toughness starts from a specimen that already has a sharp crack and measures the critical K, in MPa√m. The table summarizes the three measures:

Measure	What it measures	Unit	Test
Modulus of toughness	energy per volume up to fracture, without a crack	J/m³ (MJ/m³)	tensile test (area under the curve)
Impact energy	energy to break a V-notched specimen in a single blow	J	Charpy or Izod (ASTM E23)
Fracture toughness	critical K for a sharp crack to grow	MPa√m (ksi√in)	pre-cracked specimen (ASTM E399, E1820)

The common textbook question "name two different methods for measuring toughness" has a direct answer: the Charpy impact test (energy, in J) and the fracture toughness test on a pre-cracked specimen (K_Ic to ASTM E399, or J and CTOD to ASTM E1820). A third is the area under the tensile test curve. The formula for toughness as energy, U_T = ∫σ dε, and its units are in the article on toughness of materials; the Charpy and Izod tests, in the article on the impact test.

In structural engineering the two ideas complement each other. Toughness as energy tells whether the material deforms and gives warning before it fractures; fracture toughness tells what crack the structure tolerates under the design stress, and it is what defines the size of defect that inspection must be able to find.

Fracture toughness formula and units

The fracture toughness formula is K_Ic = Y·σ_c·√(π·a): the value of K that the combination of stress σ_c and a crack of size a must reach for fracture to occur. The same relation, solved differently, gives the stress a cracked part can carry and the largest defect it tolerates. The test uses another form of the equation, specific to each test specimen, which appears in the section on the test.

Stress intensity factor: K = Yσ√(πa)

The stress intensity factor K measures the intensity of the stress field at the tip of a crack. In the form used in design, K = Y·σ·√(π·a), where σ is the nominal stress applied far from the crack, a is the crack size and Y is a dimensionless geometry factor. Two conventions prevent the most frequent mistake in calculations:

• Edge crack (starts at the surface): a is the depth. In a wide plate, Y ≈ 1.12 (MechaniCalc).
• Internal or center crack (through the plate, away from the edges): a is half the total length. In a wide plate, Y ≈ 1 (NDE-ED).

Fracture occurs when K, which increases with stress and with crack size, reaches the K_Ic of the material. It is the same kind of comparison as between stress and strength: K is the "load" and K_Ic is the "resistance", both in MPa√m.

Fracture stress and critical crack size

Isolating the variables in the formula gives the two relations used in design. The fracture stress of a part with a crack of size a is σ_c = K_Ic / (Y·√(π·a)). The critical crack size under stress σ is a_c = (1/π)·(K_Ic / (Y·σ))².

An example shows the order of magnitude (Biopdi calculation). A 4340 steel with K_Ic = 50 MPa√m (value from English Wikipedia for this alloy) works at 600 MPa with an edge crack (Y = 1.12). The critical size is a_c = (1/π)·(50 / 672)² = 0.00176 m, or 1.76 mm. Conversely, if inspection found a 1.0 mm edge crack, the fracture stress is σ_c = 50 / (1.12 × √(π × 0.001)) = 796 MPa. Because a_c falls with the square of the stress, doubling the working stress cuts the tolerable crack to one quarter.

This calculation is what makes fracture toughness central to damage-tolerant design: with the critical size known, engineers choose an inspection method able to find cracks much smaller than a_c and, together with the fatigue crack growth rate, define the interval between inspections. A critical crack exercise on a 7075-T651 aluminum plate with an internal crack is in the article on toughness.

Units and symbol

The SI unit of fracture toughness is MPa√m (megapascal times square root of meter), equal to MN·m^-3/2; in the United States, ksi√in is used. The square root of length comes from the formula itself: stress multiplied by the square root of the crack size. The conversion, with 1 ksi = 6.89476 MPa and √(0.0254 m) = 0.15937 (Biopdi calculation), is:

• 1 ksi√in = 1.0988 MPa√m;
• 1 MPa√m = 0.9101 ksi√in.

Two related quantities use a unit of energy per area. The energy release rate G, the energy available per unit area of new crack, relates to K by G = K²/E′, where E′ = E in plane stress and E′ = E/(1 − ν²) in plane strain (NDE-ED); the critical value is G_Ic, in J/m² or kJ/m². The J-integral (Rice, Journal of Applied Mechanics, 1968) generalizes G to materials that yield and uses the same unit. E is the modulus of elasticity and ν is Poisson's ratio. The table brings together the formulas in this guide:

Quantity	Expression	Unit	Source
Stress intensity factor	K = Y·σ·√(π·a)	MPa√m	Irwin (1957); NDE-ED
Fracture stress	σc = KIc / (Y·√(π·a))	MPa	NDE-ED
Critical crack size	ac = (1/π)·(KIc / (Y·σ))²	m	NDE-ED; MechaniCalc
Minimum thickness and crack (classic)	B, a ≥ 2.5·(KIc / σys)²	m	NDE-ED; Wikipedia
Plastic zone, plane stress	rp ≈ (1/π)·(K / σys)²	m	MechaniCalc
Plastic zone, plane strain	rp ≈ (1/3π)·(K / σys)²	m	MechaniCalc
KQ for C(T)	KQ = PQ / (B·√W) · f(a/W)	MPa√m	Srawley (1976)
KQ for SE(B)	KQ = PQ·S / (B·W1.5) · f(a/W)	MPa√m	Srawley (1976)
Energy and K	G = K²(1 − ν²) / E (plane strain)	J/m²	NDE-ED

Plane strain and plane stress: why thickness matters

Plane strain fracture toughness is K_Ic: the lowest toughness value the material shows, measured at a thickness large enough that the material at the crack tip cannot deform in the through-thickness direction. In thin sheet, the material near the faces contracts freely, the crack tip yields more, and the measured toughness (called K_C, the plane stress toughness) comes out higher. As thickness increases, the core of the part is constrained by the surrounding material, the stress state becomes triaxial and the measured value drops to a plateau. That plateau is K_Ic (NDE-ED).

The diagram below shows this drop of K_C with thickness B and the appearance of the fracture surface on each side of the minimum thickness. In thin sheet (a), the fracture is slanted at about 45°, entirely in shear. In thick plate (b), the center breaks flat, perpendicular to the load, leaving only narrow shear lips next to the faces. Looking at the fracture surface is a first clue to which regime the test reached.

The size of the plastic zone explains the criterion. The plastic zone at the crack tip has an approximate radius r_p ≈ (1/π)(K/σ_ys)² in plane stress and about one third of that in plane strain (MechaniCalc), where σ_ys is the yield strength. For LEFM to hold, this zone must be small compared with the thickness, the crack and the ligament (the uncracked part, W − a). The classic criterion, cited by NDE-ED and English Wikipedia, requires B ≥ 2.5·(K_Ic/σ_ys)² and a ≥ 2.5·(K_Ic/σ_ys)². The factor 2.5 makes the thickness about 25 times larger than the plane strain plastic zone. According to a NASA analysis of the development of E399 (Tilson, 2018), recent editions of the standard mainly assess the ligament W − a with this same factor.

The practical consequence is significant, because the minimum thickness grows with the square of the ratio K_Ic/σ_ys. For a high-strength steel with K_Ic = 50 MPa√m and σ_ys = 1,500 MPa, 2.8 mm is enough; for a tough structural steel with K_Ic = 150 MPa√m and σ_ys = 500 MPa, 225 mm would be needed (Biopdi calculation). A test specimen of that size is impractical, which is why tough materials are tested with the J-integral or CTOD, as explained in the section on those parameters.

For design, the rule that follows has two sides. Using K_Ic for a thin sheet is conservative, because the thin sheet carries more than K_Ic suggests. Using the K_C of a thin sheet for a thick part is unsafe, because the thick part will fracture at the lower plateau.

How a fracture toughness test is performed

A fracture toughness test slowly loads a notched and fatigue pre-cracked test specimen and records force against crack mouth opening measured with a clip gauge. From this it calculates a provisional value, K_Q, which is accepted as K_Ic only if the validity criteria are met. The subsections follow the order of the work in the laboratory: the specimen, the pre-crack, loading and recording the curve, the calculation and the validity check.

C(T) and SE(B) specimens

The two most widely used specimens are the compact tension specimen, C(T), and the single edge notched bend bar in three-point bending, SE(B) (single edge bend, also called SENB). ASTM E399 also accepts the disk-shaped DC(T) and the arc-shaped A(T) and A(B) specimens, used for cylindrical parts. According to the official scope summary, it covers thicknesses from 1.6 mm (0.063 in). The diagram below shows the two main geometries with the dimensions used in the calculation: crack length a, width W, thickness B and, for the SE(B), the span S between the supports, equal to 4W. In the C(T), W and a are measured from the load line through the pin holes, where the force is applied.

Each geometry needs its own fixture, which is what people look for when they search for the "E399 fixture". The C(T) is loaded in tension through pins that pass through the two holes and are mounted in clevis grips, which let the specimen rotate freely during the test. The SE(B) is tested in a three-point bending fixture with two support rollers spaced S = 4W apart and a loading roller at mid-span on the face opposite the notch. The C(T) saves material because it concentrates the crack in a small block. The SE(B) is easier to machine from bars and thick plates and is the most common geometry for welds.

The photo shows a steel SE(B) specimen mounted in three-point bending: the bar rests on two rollers, the loading roller comes down on the middle of the top face, and a clip gauge is attached to the notch mouth on the bottom face, where it measures how much the notch opens as the force rises.

Specimen orientation is part of the result. For rolled products, a two-letter code is used: L is the rolling direction, T the transverse direction and S the thickness direction. The first letter is the loading direction (normal to the crack plane) and the second is the direction in which the crack grows. A T-L result, like the one for the 7075-T7351 tested by Secat, is different from an L-T result from the same lot. The a/W ratio is also controlled: the classic criterion cited by Thermal Processing calls for a/W between 0.45 and 0.55.

Notch and fatigue pre-crack

A machined notch, however fine, has a tip radius and does not behave like a crack. So after the notch is machined, the specimen receives a fatigue pre-crack: it is loaded cyclically, usually at room temperature (TWI), until a sharp crack grows from the notch tip and reaches the required length. The mechanical testing course notes from USP-EEL give a load ratio R between −1 and +0.1 for this step. The standard also limits the maximum K of the cycles to a fraction of the expected value, so that the plastic zone left by fatigue does not artificially raise the result.

Pre-cracking requires a cyclic loading machine, with force control and a frequency suited to the number of cycles, which is usually high. It is a separate step from the fracture test itself, and many laboratories do it on a different machine from the one used for the final loading. The phenomenon itself, crack growth under repeated loading, is covered in the article on fatigue testing.

In other materials the crack is produced differently. In plastics, under ASTM D5045, the notch is commonly finished with a sharp blade. For advanced ceramics, ASTM C1421 provides three routes: the beam pre-cracked with a compression bridge (pb method), the surface crack made by Knoop indentation (sc method) and the chevron notch (vb method).

Loading and recording force vs. opening (CMOD)

The pre-cracked specimen goes into the testing machine and is loaded monotonically, with slow, increasing displacement, until fracture or until it passes the maximum force. For ASTM E399, according to Wikipedia, the rate of increase of K is between 0.55 and 2.75 MPa√m/s. During loading, two signals are recorded at the same time: force, by the load cell, and the notch mouth opening, the CMOD (crack mouth opening displacement), by the clip gauge.

The clip gauge is an extensometer with two arms that seat on knife edges attached to (or machined into) the edges of the notch mouth. When the crack opens, the arms move apart and the transducer measures that opening. The result is a force vs. CMOD curve, and every number in the test comes from it. Crosshead displacement cannot replace the clip gauge, because it includes the deformation of the rollers, the pins and the machine itself.

5% secant, P_Q and K_Q

The force used in the calculation is not, in general, the maximum force. ASTM E399 defines a provisional force P_Q using the 5% secant construction: a line is drawn through the origin with a slope 5% lower than that of the initial linear portion of the curve, and the point where this line intersects the curve is P_Q (if the curve has a peak before that intersection, the peak is P_Q). The 5% reduction in slope corresponds approximately to an apparent crack extension of about 2%, which is the extension E399 associates with K_Ic.

The graph below uses the numbers from example 2 in this guide: the curve rises in a straight line, starts to bend when the crack begins to grow, crosses the dashed secant at P_Q = 4.00 kN and reaches the maximum force P_max = 4.30 kN shortly before fracture. The dotted line is the tangent to the linear portion, and the dashed line is the secant with a 5% lower slope.

With P_Q and the measured dimensions, K_Q, the provisional toughness value, is calculated. The expressions for the E399 specimens are Srawley's (International Journal of Fracture, 1976), written as functions of α = a/W:

• C(T): K_Q = P_Q / (B·√W) · f(α), with f(α) = (2 + α)(0.886 + 4.64α − 13.32α² + 14.72α³ − 5.6α⁴) / (1 − α)^1.5. At α = 0.50, f = 9.659.
• SE(B): K_Q = P_Q·S / (B·W^1.5) · f(α), with f(α) = 3√α·[1.99 − α(1 − α)(2.15 − 3.93α + 2.7α²)] / [2(1 + 2α)(1 − α)^1.5]. At α = 0.50, f = 2.6625.

With P_Q in MN and the dimensions in meters, K_Q comes out in MPa√m. The crack length a is measured after the test on the fracture surface, where the fatigue pre-crack band can be told apart from the final fracture; the average of several readings along the crack front is used.

When K_Q becomes K_Ic

K_Q is reported as K_Ic only if the test passes the validity criteria, which check that fracture actually occurred in the linear-elastic regime and under plane strain. The main ones, with figures from open sources:

Criterion	Limit	Why it exists	Source
Maximum force vs. PQ	Pmax / PQ ≤ 1.10	a strongly curved trace indicates too much plasticity	Wikipedia; USP-EEL; Thermal Processing
Specimen size	B and W − a (or a) ≥ 2.5·(KQ/σys)²	small plastic zone, plane strain	NDE-ED; NASA (Tilson, 2018)
a/W ratio	0.45 to 0.55 (classic criterion)	range in which f(a/W) is well defined	Thermal Processing
Minimum thickness covered	1.6 mm (0.063 in)	scope limit of E399-24	scope summary, ASTM

If any criterion fails, the result is reported as an invalid K_Q, not as K_Ic. The way forward is to test a larger specimen or change method and measure J or CTOD. A NASA report on E399 (Tilson, 2018) shows the effect with real data: in the same material, a C(T) with W = 38.1 mm and B = 9.5 mm gave K_Q = 38.1 MPa√m, rejected by the ligament criterion, while a C(T) with W = 76.2 mm and B = 19.0 mm gave K_Q = 44.8 MPa√m, valid. The small specimen underestimated toughness by about 15%. Biopdi recalculated both values with Srawley's expression, and they agree with the report.

Step-by-step procedure in the laboratory and what goes in the report

The procedure below summarizes the K_Ic test as it is done in a materials laboratory, including in fracture mechanics lab classes. It does not replace the standard: the exact values for each step are given in ASTM E399 or ISO 12135.

1. Choose the standard based on the material: metal with linear-elastic behavior, ASTM E399; ductile metal, ASTM E1820 or ISO 12135; weld, ISO 15653; plastic, ASTM D5045; advanced ceramic, ASTM C1421.
2. Estimate the specimen size with 2.5·(K_Ic/σ_ys)², using an expected K_Ic from the literature, and choose between C(T) and SE(B).
3. Machine the specimen and the notch in the specified orientation (L-T, T-L, etc.), with the notch at the planned position and depth.
4. Fatigue pre-crack the specimen on a cyclic loading machine until a/W is in the desired range, respecting the standard's maximum K limit.
5. Measure B and W and mount the specimen in the fixture: pin-loaded grips for the C(T), three-point bending with S = 4W for the SE(B).
6. Attach the clip gauge to the knife edges at the notch mouth and zero force and opening with the specimen unloaded.
7. Load with slow, constant displacement, within the standard's K rate, recording force vs. CMOD until fracture or past the maximum force.
8. Measure the crack on the fracture surface, as the average of several readings across the thickness, and calculate a/W.
9. Calculate P_Q and K_Q and check validity: P_max/P_Q, a/W and the size criterion.
10. Report: standard and edition, material, heat treatment and orientation, temperature, dimensions B, W and a, P_Q, P_max, the force vs. CMOD curve and the result as a valid K_Ic or an invalid K_Q, stating the criterion that failed.

KIc, J-integral and CTOD: which to use

K_Ic, the J-integral and CTOD are three fracture toughness parameters: K_Ic applies when the material fractures in an essentially elastic regime, while J and CTOD are used when there is significant plasticity at the crack tip. The split corresponds to two branches of fracture mechanics. Linear-elastic fracture mechanics (LEFM), based on K, covers high-strength steels, aerospace aluminum alloys, ceramics and glassy polymers. Elastic-plastic fracture mechanics (EPFM), based on J and CTOD, covers structural, pipeline and pressure vessel steels, for which a valid K_Ic would require enormous specimens.

The J-integral is the generalized energy release rate for a material that yields plastically. In the elastic regime, J = G, and a critical J can be converted into an equivalent K, called K_JIc. According to Wikipedia, J is accepted when the smaller of B and the initial ligament is at least 25·J_Q/σ_ys, a much smaller requirement than for K_Ic: this is what makes it possible to measure the toughness of a tough steel with a laboratory-sized specimen. CTOD (crack tip opening displacement, δ) is the opening at the crack tip at the critical instant, in millimeters, and is traditional in weld qualification and the offshore industry.

When the crack grows stably before fracturing, toughness increases as it advances, and the result becomes an R-curve (J-R or δ-R), the resistance as a function of crack extension Δa. ASTM E1820 measures K, J and CTOD both as point values and as R-curves; ASTM E561 covers K-R curves, used for thin sheet. For CTOD, TWI classifies the critical value by the behavior of the curve: δ_c when fracture is unstable without appreciable stable crack growth, δ_u when it is unstable after some stable growth, and δ_m when the test reaches a maximum force plateau without instability. The same logic applies to J (J_c, J_u, J_m). The table compares the parameters:

Parameter	When to use	Unit	Standard
KIc	linear-elastic fracture, plane strain; high-strength steel, aluminum, ceramic, glassy polymer	MPa√m	ASTM E399; ISO 12135
GIc	same regime as KIc, expressed as energy; common for polymers and composites	J/m² (kJ/m²)	ASTM D5045 (plastics)
J (JIc, J-R curve)	significant plasticity; structural and pipeline steels	kJ/m²	ASTM E1820; ISO 12135
CTOD (δ)	significant plasticity; welds, offshore	mm	ASTM E1820; ISO 12135; ISO 15653 (welds)

In short, the answer to the CTOD question (what is the procedure) has the same structure as the K_Ic test: a pre-cracked SE(B) or C(T) specimen, slow loading while recording force vs. opening, and calculation of CTOD from the plastic component of the measured opening, classified as δ_c, δ_u or δ_m according to the type of curve. The former US standard dedicated to CTOD, ASTM E1290, was withdrawn in 2013 (TWI), and CTOD is now measured under E1820.

Fracture toughness testing standards

The ASTM standard for fracture toughness testing of metals is ASTM E399 (K_Ic), complemented by ASTM E1820 (J, CTOD and K). ASTM D5045 covers plastics, ASTM C1421 covers advanced ceramics, and the international reference for metals is ISO 12135. The table lists each standard with the edition and status we checked in the ASTM store on 10/13/2026. We could not check the ISO editions in the ISO catalog on that date, so they appear without a year.

Standard and edition	Material and test specimen	What it measures	Status on 10/13/2026
ASTM E399-24	metals; SE(B), C(T), DC(T), A(T), A(B); thickness from 1.6 mm	plane-strain KIc	current, no newer edition
ASTM E1820-25d, editorial revision ε2	metals; SE(B), C(T), DC(T)	J, CTOD and K, as a point value or R-curve	current; 25d without the ε2 revision is historical
ASTM D5045-14(2022)	plastics; SENB and CT	KIc and GIc, linear-elastic behavior	current
ASTM C1421-18(2025)	advanced ceramics; precracked beam, Knoop surface crack, chevron notch	KIpb, KIsc, KIvb	current
ASTM E1921-25a	ferritic steels in the ductile-to-brittle transition	reference temperature T0 (master curve)	current; 25 is historical
ISO 12135	metals; fatigue-precracked specimens	K, CTOD, J and R-curves, quasi-static	edition not checked on this date
ISO 15653	metallic welds	K, CTOD and J in welded joints	edition not checked on this date
BS 7448-1:1991	metals	critical KIc, CTOD and J	withdrawn in 2021, replaced by the British adoption of ISO 12135 (BSI)
ASTM E1290	metals	CTOD	withdrawn in 2013 (TWI)

Three points in the table are often overlooked. First, ASTM E1820 no longer calculates K_Ic: since the 2025 editions, a note in the standard states that the K_Ic evaluation was removed to avoid duplication and refers the user to E399. If you need K_Ic, use E399; if you need J or CTOD, use E1820. Second, the scope of E399-24 covers rapid loading in special cases as well as slow loading. Third, ASTM E1921 does not measure K_Ic: it determines the master curve reference temperature T₀ of ferritic steels with yield strength from 275 to 825 MPa, using at least six test specimens and a loading rate of 0.5 to 2 MPa√m/s, according to the scope summary.

ASTM E647 shows up in lists of "toughness tests", but it is not one of them: it measures the fatigue crack growth rate, da/dN, as a function of the range of K. Together with K_Ic, it is the standard that lets you calculate how long a crack takes to reach critical size. Likewise, the Charpy test (ASTM E23) is an impact test, not a fracture toughness test.

Brazilian standards. We found no ABNT (Brazilian) standard equivalent to ASTM E399 or ISO 12135. Laboratories in Brazil test to the ASTM and ISO standards and get the test accredited under ABNT NBR ISO/IEC 17025 (the Brazilian adoption of ISO/IEC 17025), as Reguly and Fabricio report (ABM Annual Congress, 2015) in an intralaboratory study of K_Ic.

Typical fracture toughness values

Fracture toughness ranges from less than 1 MPa√m in glass and glassy polymers to more than 150 MPa√m in high-toughness steels, a span of more than two orders of magnitude. The table gives ranges by material class at room temperature. The ksi√in column is a Biopdi conversion. The ranges are wide because K_Ic depends on the alloy, heat treatment, orientation and thickness. For design, the value must come from testing the actual material.

Material	KIc (MPa√m)	KIc (ksi√in)	Source
Maraging steel, grade 200	175	159	Wikipedia (EN)
Titanium alloys	84 to 107	76 to 97	Wikipedia (EN)
Inconel 718	73 to 87	66 to 79	Wikipedia (EN)
4340 alloy steel	50	45.5	Wikipedia (EN)
7075 aluminum	20 to 35	18 to 32	Wikipedia (EN)
7075-T7351 aluminum, T-L, measured	30.5	27.8	Secat
Aluminum alloys, general range	14 to 28	12.7 to 25.5	Wikipedia (EN)
Alumina (Al2O3)	3 to 5	2.7 to 4.6	Wikipedia (EN)
Silicon carbide	3 to 5	2.7 to 4.6	Wikipedia (EN)
PMMA (acrylic)	0.7 to 1.6	0.64 to 1.46	Wikipedia (EN)
Polystyrene	0.7 to 1.1	0.64 to 1.00	Wikipedia (EN)
Concrete	0.2 to 1.4	0.18 to 1.27	Wikipedia (EN)
Soda-lime glass	0.7 to 0.8	0.64 to 0.73	Wikipedia (EN)

The Secat value comes from an actual test: a 7075-T7351 in the T-L orientation gave a K_Q of 27.8 ksi√in (30.5 MPa√m), within the range of 25 to 33 ksi√in (27.5 to 36.3 MPa√m) that the company cites from the ASM Handbook. Three rules apply when reading the table. Within the same alloy family, higher strength usually comes with lower fracture toughness, and heat treatment shifts the value in either direction (see heat treatment of metals). Orientation changes the value in rolled and forged products. Temperature matters most in ferritic steels, which go through a ductile-to-brittle transition. A table from Dowling with the yield strength alongside the K_Ic of ten metallic alloys is in the article on toughness.

For polymers, which come up in searches such as "polymer toughness measurement", the test is ASTM D5045, with results reported as K_Ic and G_Ic. The low values for PMMA and polystyrene explain why acrylic parts crack from holes and sharp corners: with a K_Ic close to 1 MPa√m, a flaw of a few millimeters is already critical under moderate stresses.

Fracture toughness worked examples

The examples below cover using the formula in design, calculating K_Q for the two specimen types and converting units. The calculations are Biopdi's. The numbers in examples 2 and 3 are illustrative and consistent with the published ranges.

1. Does the part fracture? An alloy with K_Ic = 32 MPa√m fractures under 245 MPa when the largest internal crack is 2.89 mm long. Will it fracture under 318 MPa if the largest internal crack is 1.45 mm? Since the geometry is the same, Y cancels out and you only need to compare the two cases: K₂/K₁ = (σ₂/σ₁)·√(a₂/a₁) = (318/245) × √(1.45/2.89) = 1.2980 × 0.7083 = 0.9194. In the first case K₁ = K_Ic = 32 MPa√m, so K₂ = 0.9194 × 32 = 29.4 MPa√m. Since 29.4 is less than 32, the part does not fracture. The result is the same whether a is the full length or half of it, because only the ratio enters the calculation.

2. K_Q for an aluminum SE(B) specimen. A 7075-T651 aluminum SE(B) bar has W = 20 mm, B = 10 mm, S = 4W = 80 mm and a measured crack length a = 10 mm (a/W = 0.50). The yield strength is σ_ys = 505 MPa, the same value as in the alloy table of the toughness article. On the force vs. CMOD curve, the 5% secant gives P_Q = 4.00 kN, and the maximum force is P_max = 4.30 kN.

1. f(0.50) for SE(B): 3 × √0.5 × [1.99 − 0.5 × 0.5 × (2.15 − 3.93 × 0.5 + 2.7 × 0.25)] / [2 × (1 + 1) × 0.5^1.5] = 2.1213 × 1.7750 / 1.4142 = 2.6625.
2. P_Q·S / (B·W^1.5) = 4,000 × 0.080 / (0.010 × 0.0028284) = 1.1314 × 10⁷ Pa√m = 11.31 MPa√m.
3. K_Q = 11.31 × 2.6625 = 30.1 MPa√m (27.4 ksi√in).
4. Validity: P_max/P_Q = 4.30/4.00 = 1.075, below 1.10; a/W = 0.50, within 0.45 to 0.55; 2.5 × (30.1/505)² = 0.0089 m = 8.9 mm, and both the ligament W − a = 10 mm and the thickness B = 10 mm are larger.

Result: K_Ic = 30.1 MPa√m, within the 20 to 35 MPa√m range in the table for 7075. The 4 kN force is low, suitable for a 10 kN or 50 kN machine with a bending fixture.

3. K_Q for a steel C(T) specimen. A compact C(T) specimen has W = 50 mm, B = 25 mm and a measured crack length a = 25 mm (a/W = 0.50). The 5% secant gives P_Q = 20.0 kN, and the steel has σ_ys = 450 MPa.

1. f(0.50) for C(T): (2 + 0.5) × (0.886 + 4.64 × 0.5 − 13.32 × 0.25 + 14.72 × 0.125 − 5.6 × 0.0625) / 0.5^1.5 = 2.5 × 1.366 / 0.35355 = 9.659.
2. P_Q / (B·√W) = 20,000 / (0.025 × 0.22361) = 3.578 × 10⁶ Pa√m = 3.578 MPa√m.
3. K_Q = 3.578 × 9.659 = 34.6 MPa√m (31.5 ksi√in).
4. Size validity: 2.5 × (34.6/450)² = 0.0147 m = 14.7 mm. The ligament W − a = 25 mm and the thickness B = 25 mm pass; a/W = 0.50 passes.

Result: if the curve shows P_max ≤ 1.10 × 20.0 = 22.0 kN, K_Ic = 34.6 MPa√m. If the maximum force exceeds 22.0 kN, the value stands as an invalid K_Q, and the material should be tested by J or CTOD.

4. From K to energy and to ksi√in. A steel has K_Ic = 50 MPa√m, E = 207 GPa and ν = 0.30. In plane strain, G_Ic = K_Ic²·(1 − ν²) / E = (50 × 10⁶)² × 0.91 / (2.07 × 10¹¹) = 1.10 × 10⁴ J/m², or 11.0 kJ/m². In US customary units, 50 × 0.9101 = 45.5 ksi√in. Converting to G is useful for comparing steel with polymers and composites, whose toughness is usually published in kJ/m².

Fracture toughness and the Charpy test

The Charpy test measures the energy needed to break a small V-notched specimen in a single blow; the fracture toughness test measures the critical K of a sharp crack under slow loading. The two results cannot be converted into each other, and the existing correlations are only estimates. Three differences explain why: the Charpy notch has a 0.25 mm radius and is not a crack; the pendulum loading rate is much higher; and the specimen is too small to ensure plane strain in most steels. The impact test is covered in its own article, which also lists the limits of the correlations.

The most cited correlation is the one by Rolfe, Novak and Barsom for the upper shelf of the Charpy curve. In SI units, with K_Ic in MPa√m, σ_ys in MPa and the Charpy energy CVN in joules, it reads (K_Ic/σ_ys)² = 0.646 × (CVN/σ_ys − 0.0098), according to a document from the US NRC; Biopdi checked the coefficients by converting the original form in US customary units. The original database covered steels with yield strength from 760 to 1,700 MPa (Lehigh University report). An example: a steel with σ_ys = 800 MPa and CVN = 60 J on the upper shelf gives (K_Ic/σ_ys)² = 0.646 × (0.075 − 0.0098) = 0.0421, K_Ic/σ_ys = 0.205 and K_Ic ≈ 164 MPa√m, as an estimate.

The number is useful for screening, not for design. Outside the range of steels in the database, in the transition region or for other materials, the correlation can be far off. Ritchie, Francis and Server (Metallurgical Transactions A, 1976) studied a quenched 4340 steel in which austenitizing at 1,200 °C instead of the conventional 870 °C doubled K_Ic while reducing the Charpy energy: the two measures can move in opposite directions, and the authors conclude that toughness should not be assessed by only one of them.

Common mistakes in fracture toughness testing

The mistakes that most distort the result, or how it is read:

1. Calling any K_Q a K_Ic. Without passing the validity criteria, the value is K_Q and depends on the specimen.
2. Calculating K_Ic to ASTM E1820. Since 2025, E1820 refers K_Ic to E399.
3. Using an incomplete K_Q formula. For C(T), K_Q = P_Q/(B·√W)·f(a/W); for SE(B), P_Q·S/(B·W^1.5)·f(a/W). Writing "P·B·W" without the square root and without the division gives a number with no physical meaning.
4. Using the maximum force instead of P_Q without checking the P_max/P_Q ratio.
5. Using crosshead displacement instead of CMOD, which includes roller play and machine compliance.
6. Skipping or shortening the fatigue pre-crack and testing with only the machined notch: the notch radius raises the result.
7. Applying K_Ic to thin sheet, or a thin-sheet K_C to a thick part. The first is conservative; the second is unsafe.
8. Using the full length of an internal crack as a. For an internal crack, a is half the length.
9. Leaving out orientation and temperature in the report and when comparing lots.
10. Using Charpy energy as the design K_Ic. The correlation is an estimate.
11. Citing withdrawn editions or standards as current, such as ASTM E399-22, ASTM E1290 or BS 7448-1.
12. Mistaking ASTM E647 for a toughness test. It measures fatigue crack growth (da/dN).
13. Mistaking the blue fracture test for fracture toughness. The blue fracture test (ISO 3763; ABNT NBR 6346, the Brazilian standard) reveals non-metallic inclusions in steel: the specimen is fractured in the blue brittleness range, around 300 to 350 °C, and it does not measure K_Ic.

Machine for fracture toughness testing

The final loading in a fracture toughness test is done on a testing machine with a load cell, slow displacement control, a three-point bend fixture (SE(B)) or pin-loading clevises (C(T)), and a clip gauge to measure the CMOD. The fatigue pre-crack, made beforehand, requires a cyclic loading machine. The Biopdi universal testing machine, with the bend fixture and the COD clip gauge, covers the quasi-static part of the SE(B) test: the Biopdi website lists fracture toughness to ASTM E399 among the applications of the clip gauge. Biopdi does not claim to perform fatigue pre-cracking or to supply clevises for C(T) specimens. The panel below shows the machine, the role of each part in the test and the two accessories used in the SE(B) setup.

The machine is chosen by the expected force. In the examples in this guide, P_Q is 4 kN for the aluminum SE(B) and 20 kN for the steel C(T); in the NASA case, 7 to 21 kN. This force range fits the single-column machine up to 10 kN, for small specimens and polymers, and the dual-column machine from 5 to 50 kN, for most laboratory metallic specimens. The table summarizes the models in this range:

Application	Range	Biopdi model
Small SE(B), polymers (D5045)	2 to 10 kN; 0.01 to 500 mm/min	MBIOI-10-M2
Metal SE(B), forces up to tens of kN	5 to 50 kN; 0.01 to 500 mm/min	MBIOII-50-M2
Larger specimens	100 to 200 kN; 0.01 to 500 mm/min	MBIOII-200-M2

The clip gauge is chosen by the gauge length between the arms, which must fit the knife edges at the notch mouth, and by the travel, which must exceed the maximum expected opening. The expected opening depends on the specimen size and the plasticity of the material; the longer-travel models also serve fiber-reinforced concrete beams tested to EN 14651. The four models in the family, according to the extensometers page:

Code	Initial gauge length L0	Travel
EXT-400-001	5 mm	+2.5 mm
EXT-400-003	10 mm	+4 mm
EXT-400-004	12 mm	+7 mm
EXT-400-005	20 mm	+12 mm

P_Q, K_Q and validity are calculated according to the applicable standard, from the recorded force × CMOD curve. Fracture toughness is one of the mechanical tests performed on the same universal testing machine; the guide on how to choose a universal testing machine compares models and configurations, and the overview of the mechanical properties of materials helps decide which tests to request together.