fracture mechanics

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Fracture Toughness Testing of Metals

FRACTURE TOUGHNESS TESTING OF METALS

Contents

• Background

• Specimen Configurations

• Specimen Orientation

• Fatigue Precracking

• Instrumentation

• Side Grooving

• Plain Strain Fracture Toughness

• K-R Curves


Background

• Those who approach fracture from a solid mechanics/ structural mechanics

viewpoint, often sidestep microstructural issues and consider only continuum

models.

• In certain cases, classical Fracture Mechanics provides some justification for

disregarding microscopic failure mechanisms. When a single parameter (i.e.

G, K, J or CTOD) uniquely characterizes crack tip conditions, a critical value

of this parameter is a material constant that is transferable from a laboratory

test specimen to a structure/ component made from the same material.

• The situation becomes considerably more complicated when a fracture

toughness test on a small lab test specimen is no longer a reliable indicator of

how a complex structure/ component will behave. A single parameter

assumption ceases to be valid. The two configurations may even fail by

Background

different mechanisms. A number of researchers are attempting to develop

alternatives to single parameter fracture mechanics for such cases.

• A fracture toughness test measures the Resistance of a Material to crack

extension. Such a test may yield a single value of fracture toughness or a

Resistance Curve, where a toughness parameter ( K, G, J, CTOD) is plotted

against Crack Extensions.

• A variety of organizations throughout the world publish standard procedures

for fracture toughness measurements, including ASTM, BSI, ISO, JSME, etc.

The first standard for K testing was developed by ASTM in 1970 and for J

testing in 1981. BSI published the CTOD test method in 1979.

• Existing fracture toughness test standards include procedures for KIC , K-R

Curve, JIC , J-R Curve, CTOD and KId testing. We primarily focus on ASTM

standard test procedures.

Background

• The reader should not rely on text books alone for guidance on conducting

fracture toughness tests, but should consult the relevant standards. Also the

reader should gain an understanding of the fundamental basis of G, K, J and

CTOD as well as the limitations of these to characterize the fracture

toughness of new materials. Ex: laminated fibre reinforced polymer matrix composites.

• All fracture toughness tests have several common features. The design of test

specimens is similar in each standard; and the orientation of the specimen

relative to symmetry directions in the material is always an important

consideration. The cracks at the root of a notch in the test specimens are

induced by fatigue in each case; the basic instrumentation to measure load

and displacement is common; but some tests require additional

instrumentation to monitor crack growth.


Specimen Configurations

• Fig 7.1 shows commonly recommended test specimen types.

• Each test specimen has three important characteristics dimensions: crack

length (a), thickness (B) and width (W). In most cases, W=2B and a/W 0.5

• There are a number of configurations that are used in RESEARCH, but not

yet standardized. They are single edge notch tensile panel, the double edge

notched tensile panel, the axisymmetric notched bar, and the double

cantilever beam specimen.

• The compact specimen is pin- loaded by special clevises, as illustrated in

fig 7.2.

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Specimen Configurations


Specimen Orientation

• Specimen orientation is such an important variable in fracture toughness

measurements, all ASTM standard featured test methods require that the

orientation be reported along with the measured fracture toughness;

ASTM has adopted a notation for this.

• Fig 7.5 illustrates the ASTM notation for fracture specimens extracted from a

rolled plate or a forging. There are six recommended orientations. The letters

L, T, and S denote the Longitudinal, Transverse and Short transverse

directions, relative to the rolling direction or the forging axis.


• Two letters are used to identify the orientation of the test specimen; the first

letter indicates the loading direction (which is always normal to the crack

plane in mode I loading) and the second letter denotes the direction of crack

propagation. For example, the L-T orientation corresponds to loading in the

Longitudinal direction and crack propagation in the Transverse direction.

• A similar notation applies to round bars and hollow cylinders, as fig 7.6

illustrates. The symmetry directions in this case are Circumferential, Radial

and Longitudinal (CRL) respectively.

• Ideally, one should measure the toughness of a material in several

orientations, but this is often not practical.


Fatigue Precracking

• LEFM applies to cracks that are infinitely sharp prior to loading. While lab

test specimens invariably fall short of this ideal, it is possible to induce cracks

that are sufficiently sharp for practical purpose. The most efficient way to

produce such a cracking is through cyclic loading.

• Fig 7.7 illustrates the precracking procedure in a typical specimen where a

fatigue crack initiates at the root of a machined notch and grows to the

desired length through careful control of the cyclic load (amplitude and

number of cycles).

• The fatigue crack should not adversely influence the fracture toughness

measured. Cyclic loading produces a crack with a finite tip radius and a small

plastic zone at the crack tip, which contains strain hardened material and a

complex residual stress distribution.

Fatigue Precracking

Fatigue Precracking

In order for a measured fracture toughness to reflect true material properties,

the fatigue precracking must satisfy the following conditions:

a. The crack- tip radius at FRACTURE must be much larger than the initial

radius of the fatigue crack.

b. The plastic zone produced during fatigue cracking must be small compared

to the plastic zone at Fracture.

• In KIC testing, the maximum crack tip SIF during fatigue loading must be no

greater than a specified fraction of KIC.

• Of course one can always perform fatigue precracking well below the

allowable loads in order gain assurance of the validity of the results, but the

TIME required to produce the crack (i.e. the number of load cycles) increases

rapidly with decreasing load amplitudes.


Instrumentation

• At a minimum, the applied LOAD and a characteristic displacement of the

specimen must be measured during a fracture toughness test. Additional

instrumentation is required to monitor crack growth or to measure more than

one displacement.

• Measuring load during fracture toughness test is straight forward, since all

testing machines are equipped with load cells.

• The most common displacement transducer in fracture toughness tests is the

clip gauge, illustrated in fig 7.8. The clip gauge, which attaches to

the mouth of the crack, consists of four electrical resistance strain gauges

bonded to a pair of cantilever beams. Deflection of the beams results in a

change in the resistances of the strain gauges, which varies linearly with the

displacement. A clip gauge must be attached to sharp knife edges in order to

Instrumentation

Instrumentation

ensure that the ends of each beam are free to rotate. The knife edges can

either be machined into the specimen or attached to the specimen at the crack

mouth.

• A Linear Variable Differential Transformer (LVDT) provides an alternative

means for measuring displacements in fracture toughness tests.

• Fig 7.10 illustrates the potential drop method for monitoring crack growth.

• The unloading compliance technique allows crack growth to be inferred from

the LOAD and DISPLACEMENT measuring transducers that are used in a

standard fracture toughness test. A test specimen can be partially unloaded at

various points during the test in order to measure the elastic compliance,

which can be related to the crack length.

Instrumentation

Instrumentation

• In some cases it is necessary to measure more then one displacement on the

same test specimen. For example, one may want to measure both crack mouth

opening displacement (CMOD) and the displacement along the load axis. A

compact tension specimen can be designed such that the load line

displacement and the CMOD are identical, but these two displacements do

not coincide in a Single Edge Notched Bend specimen (SENB). Fig 7.11

illustrates simultaneous CMOD and load line displacement measurement in a

SNEB specimen.

Instrumentation


Side Grooving

• Figure 7.12 illustrates grooves machined into the sides of a fracture toughness

test specimen. The purpose is to maintain a straight crack front during an

R- Curve test. Side grooves remove the free surfaces, where PLANE

STRESS conditions prevail and lead to relatively straight crack fronts.

Typical side- grooved fracture toughness test specimens have a net thickness

that is ~ 80% of the gross thickness.

Side Grooving


Plane Strain Fracture Toughness

(Critical Mode I Stress Intensity Factor KIC)

• When a material behaves in a linear elastic manner prior to FRACTURE,

such that the crack tip plastic zone size is small compared to specimen

dimensions, a critical value of the mode I SIF, namely KIC, may be an

appropriate Fracture parameter. i.e. Fracture in a structure/ component occurs

when KI = KIC.

• The ASTM standard E 399 to measure KIC was first published in 1970, and

has been revised several times since then.

The title: Standard Test Method for Plane Strain Fracture Toughness of

Metallic Materials.

Plane Strain Fracture Toughness • Four test specimen configurations are permitted by the current version of

E 399. The Compact Tension Specimen (CTS), The Single Edge Notched

Bending Test, A C shaped specimen and Disk - shaped specimen.

• If the plastic zone at FRACTURE is too large, it is not possible to obtain a

valid KIC.

• ASTM E 399 recommends that the user perform validity check to determine

the appropriate specimen dimensions. The test - specimen size requirements

for a valid KIC are:

B, a 2.5 (KIC / YS)2

0.45 (a/w) 0.55

So the user must know a priori the KIC! (Beg, borrow or steel)

ASTM standard provides a table of recommended thickness for various

strength levels.


• There is not a unique relationship between KIC and YS in metals.

• During Fatigue Pre-cracking, the peak value of the SIF in a single cycle, Kmax, should be no larger than 0.8 KIC, according to ASTM E 399.

• When a pre-cracked test specimen is loaded to failure, “load” and

“displacement” are monitored. Three types of load - displacement curves are

shown in fig 7.13 during a KIC test. The critical load PQ, is defined in one of

several ways, depending on the type of curve. One must construct a 5%

secant line (i.e. a line from the origin with a slope equal to 95% of the initial

elastic loading slope) to determine P5. In the case of type I behavior, the load

- displacement curve is smooth and it deviates slightly from linearity before

final FRACTURE at Pmax. This NON-LINEARITY can be caused by

plasticity, subcritical crack growth, or both. For a type I curve PQ = P5. With a

type I curve, a small amount of unstable crack growth (i.e. a pop-in) occurs

before the curve deviates from linearity by 5%. In this case, PQ is defined at


the pop-in. A test specimen that exhibits type III curve FRACTURES

completely before achieving 5% non-linearity. In this case, PQ = Pmax.

• The crack length ‘a’ must be measured after the test from the fracture surface.

Since there is a tendency for the crack length to vary through the thickness,

the crack length ‘a’ is defined as the average of three evenly spaced

measurements. Once PQ, and ‘a’ are determined, a provisional fracture

toughness, KQ, is calculated from the following equation:

KQ = {PQ / BW} f(a/W)

where f(a/w) is a dimensionless function of (a/W). This function is given in

POLYNOMIAL form in ASTM E 399 standard for the four test specimen

types. They are also tabulated in ASTM E 399.


• Now perform validity checks

0.45 (a/W) 0.55 -----(a)

B, a 2.5 (KIC / YS)2 -----(b)

Pmax 1.10 PQ -----(c)

If the test meets all of the requirements of ASTM E 399, then KQ = KIC.

• Consider a fracture toughness test that displays considerable plastic

deformation prior to fracture. Fig 7.14 illustrates the load – displacement

curve for such a case. Since this is a type I curve, PQ = P5. KQ value

calculated using PQ may just barely satisfy the size requirements namely

B, a 2.5 (KQ / YS)2

KQ here would have little relevance as the actual fracture toughness of the

material, since the specimen fractures well beyond PQ; the KQ value here

would grossly under estimate the true toughness of the material.

Consequently the third validity requirement, namely Pmax 1.10 PQ, is

necessary to ensure that KIC value is indicative of the true toughness of the

material.


• Because the test specimen size requirements of ASTM E 399 are very

stringent, it is very difficult and sometimes impossible to measure a valid KIC

in most engineering materials. A material must either be relatively brittle or

the test specimen must be very very large for LEFM to be applicable. In low

and medium strength structured steels, valid KIC measurements are normally

possible only on the lower shelf of fracture toughness; in the ductile – brittle

transition and the upper shelf, EPFM should be used and parameters such as

the path independent integral J and the crack tip opening displacement

(CTOD) are required to characterize FRACTURE.

• Example I: Structural steel; YS = 350 MPa (51 ksi). Estimate CT specimen

dimensions for a valid KIC test.

Estimated Toughness: KIC = 200 MPa m

B, a = 2.5(200 MPa m / 350 MPa)2

= 0.816 m (32.1 in)!

Since a/W = 0.5, W = 1.63 m (64.2 in)!


Thus a very large test specimen would be required for a valid KIC test. The

material is seldom available in such thickness. Even if a sufficiently large

thickness specimen were fabricated, testing would not be practical; machining

would be probablively expensive, and a special purpose testing machine with

a high load capacity would be needed.

• Conclusion: SIF is not a suitable parameter to characterize the fracture

toughness of such a material. We should try J or CTOD.


SIF (K) vs Crack Growth Resistance (R) Curves (K-R Curves)

• Some materials whose behavior is predominantly Linear Elastic prior to

FRACTURE exhibit a Rising R curve.

• The ASTM standard E 561 outlines a procedure for determining the SIF (K)

vs Crack growth resistance (R) curves for such materials.

• Standard E 561, unlike E 399, does nor contain a minimum thickness

requirement; and thus is applicable to test thin sheets. However, this standard

is applicable only when the plastic zone size is small compared to the in plane

dimensions of the test specimen.

• This test method is often applied to high strength sheet materials, where the

fracture occurs in a plane stress state.


• Common misconception about plane stress, plane strain, and R-curves: It is

implied that a material in plane strain state exhibits a single value of fracture

toughness (KIC) while the same material in a plane stress state displays a

rising R curve. However, the shape of the K-R curve depends on the Fracture

Mechanism as well as the stress state at the crack tip!

• Cleavage tends to exhibit a flat or falling R curve; while micro void

coalescence can produce a Rising R curve. The slope of R curve tends to

decrease with increasing stress triaxially and the fracture mechanism (in

steels) can change from ductile tearing to cleavage as the stress state ranges

from plane stress to plane strain.

• Fig 7.15 illustrates a typical K-R curve in a predominantly linear elastic

material behavior. The R-curve is initially very steep, as little or no crack

growth occurs as the SIF K is increased. As the crack begins to grow; R

increases with crack extension until a steady state is reached, where the R


curve becomes flat. It is therefore possible to define a critical stress intensity

factor, KC, where the Crack Driving Force is tangent to the R curve. KC

however, is not a material property, because the point of tangency depends on

the shape of the driving force curve, which is governed by the geometry of

the cracked body. Thus KC values obtained using lab test specimens are not

usually transferable to structures/ components made of the same material.

• Test Specimen Design:

The ASTM standard for K-R curve testing recommends 3 configurations:

The middle tension geometry, the compact tension specimen, and a wedge

loaded compact tension specimen. The latter shown in fig 7.27 is the most

stable of the three specimen types; and thus suitable for materials with

relatively flat R curves.


• Since this test method is often applied to thin sheets, The compact tension

specimen will not have the conventional geometry, with the width (w) equal

to twice the thickness (B). The specimen thickness is fixed by the shell

thickness, and the width is governed by the anticipated toughness of the

material, as well as the available test fixtures.

• Standard fixtures can be used to test thin compact tension specimens,

provided the specimens are filled with spacers, as illustrated in fig 7.16.

• One problem with thin sheet fracture toughness testing is that the test

specimens are subjected to out-of-plane buckling, which leads to a combined

Mode I and Mode III loading of the crack. Consequently, an antibuckling

device should be fitted to the test specimen. Fig 7.16 illustrates a typical

antibuckling fixture for thin compact tension specimens. Plates on either side

of the test specimen should not be bolted too tightly together, because loads

applied by the test machine should be carried by the specimen rather than the


antibuckling plates. Some type of lubricant, e.g. Teflon sheet is usually

required to allow the specimen to slide freely through the two plates during

the test.

• The ASTM standard E 561 outlines alternative methods for computing both

KC and the crack extension in a R curve test; the most appropriate approach to

be selected depends on the relative size of the crack tip plastic zone. For the

special case of negligible plasticity, which exhibits a load - load point

displacement behavior that is illustrated in fig 7.17, as the crack grows, the

P-Δ curve deviates from its initial linear shape because the compliance

continuously changes. If the specimen were to be unloaded prior to

FRACTURE, it would return to the original as the dashed lines indicate.

• The compliance C at any point during the test is equal to the measured

displacement by the measured load.


• The instantaneous crack length can be inferred from the compliance C

through relationship that are given in the ASTM standard. The crack length

can also be measured during the test using optical techniques.

• The instantaneous SIF is computed using the current values of load P and crack length ‘a’:

KI = {P/BW} f(a/W)

• For the case where a plastic zone develops ahead of the growing crack, the

nonlinearity in the load - displacement curve is caused by a combination of

crack extension and plasticity as fig 7.18 illustrates. If the specimen is

unloaded prior to FRACTURE, the load - displacement curve does not return

to the origin; crack tip plasticity produces a finite amount of permanent

deformation in the specimen. The instantaneous crack length can be measured

using optical techniques or can be calculated from unloading compliance,

where the specimen is partially unloaded, the elastic compliance is measured


(C = Δ/P), and the crack length is inferred from compliance. The SIF should

be corrected for plasticity effects by determining an effective crack length.

aeffective ASTM standard suggests two alternative approaches for computing

aeffective (I) the Irwin plastic zone correction and (II) the Secant method.

• According to the Irwin approach, the effective crack length assuming plane

stress state is given by:

aeffective = a + 1/2 (K / YS)2

• The Secant method consists of determining an effective crack length from the

effective compliance, which is equal to the total displacement divided by the

applied load (fig 7.18).

• The effective SIF for both methods is computed using applied load P and

effective crack length aeffective:

Keff = {P/BW} f(aeff/W)


• The choice of plasticity correction is left largely to the user. When the plastic

zone is small, ASTM E 561 suggests that the Irwin’s correction is acceptable,

but recommends the Secant method when the crack tip plasticity is more

extensive.

• The ASTM K-R curve standard requires that the crack tip SIF be plotted

against the effective crack extension Δ aeff. The estimation of the instability

point (KC) should not be sensitive to the way in which the crack growth is

quantified.

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