**THE INTERPRETATION OF FRACTURE TOUGHNESS DATA**

**Johann Wannenburg**

University of Pretoria, Pretoria 0002, South Africa, and
Laboratory for Advanced Engineering (Pty) Ltd, Pretoria, South Africa

**Keywords:**
Fracture Toughness, Fracture Mechanics, Life Extension, Linear-elastic,
Elastic-plastic, Petro-chemical

**ABSTRACT**

The
rising importance of accurate fracture mechanics analyses for life extension
purposes has placed larger responsibilities on the analyst to ensure accurate
analysis inputs. Often, the most costly and confusing part of this process is
to establish the fracture toughness data. This paper presents a summary of the
different experimental methods that is used and puts into perspective the interpretation
of such results in terms of the global objectives and restraints. It is shown
that the standard methods for determining linear elastic, as well as
elastic-plastic fracture toughness parameters are largely outdated and should
be replaced with a single, unambiguous method.

**INTRODUCTION**

Fracture
mechanics has found its application for the most part, in the petro-chemical
and power generation industries, as well as the aircraft industry, where the consequence
of fracture failure makes it imperative that the existence of defects must be
accepted and the effect thereof on the integrity of the structures must be
controlled. These industries are on average and for the most part a few decades
old. The original design lives are now often approached or exceeded and current
economic and environmental concerns have put enormous pressure on extending the
operational lives of these structures beyond what was originally intended.

Designs done a few decades ago have
been based on analysis techniques that has since been improved and have
incorporated safety factors (or ignorance factors) that may now be reduced. The
life extension drive therefore implies that integrity assessments must now be
redone with increased accuracy to enable design lives of old structures to be
increased.

The
fracture mechanics analysis process essentially entails comparing the crack
driving force, which is a function of the component and crack geometry and the
loading, with the material resistance to crack propagation, which is commonly
called the fracture toughness. This comparison yields an estimation of the
critical, or allowable crack size, or the critical, safe loading for a given
crack size. The accuracy of any analysis is somewhat dependent on the inherent
accuracy of the analysis method (any analysis method is based on a mathematical
model of a real system or process, which always implies that some assumptions
and approximations are made), but is in practice largely dependent on the
accuracy of the input data.

It
can, or should be argued, that the most influential factor on the accuracy of
the analysis, is the accuracy of the estimation of the input loading. This,
however is not seen as part of the fracture mechanics science. Be it as it may,
often the most costly and confusing part of the process to establish the inputs
for a fracture mechanics analysis is the determination of the fracture
toughness data. The present paper summarizes the different experimental methods
for determining fracture toughness and puts into perspective the interpretation
of such results in terms of the global objectives and constraints.

**ANALYSIS METHODS**

**Linear
elastic fracture mechanics**

Linear
elastic fracture mechanics (LEFM) has been based on a stress field solution of
the stresses in the vicinity of an infinitely sharp crack in an arbitrary
elastic body with arbitrary loading. It was found that the stress state of any
element near the crack tip is a function of the position of the element in
relation to the crack, as well as a common parameter, called the stress
intensity factor (K).

_{} (1)

This
factor is proportional to the applied stress and inversely proportional to the
square

root
of the crack length. The proportionality factor (b)
is a function of the component

geometry
and the crack geometry:

_{} (2)

The
stress field solution implies that the elastic stresses would reach infinity at
the crack tip, which in a real material could not be the case. It is clear that
a plastic zone would exist at the tip of the crack. It has been shown that the
size of this zone is a function of K, implying that K still characterizes the
elastic/plastic stress state at the tip of the crack and therefore could be
used as a parameter to model the fracture process. This means that if K at
fracture (Kc) is known for a material, failure of a component could be
predicted if K, calculated for the specific loading and geometry of the
component, is equal to Kc.

However,
the size of the plastic zone would also depend on the constraint conditions
(ie. plane strain or plane stress), leading to the conclusion that when Kc is
determined for a material through a material test, it must be ensured that
similar constraint conditions will exist in the test specimen, than will exist
in the component for which the toughness value will be used in an analysis.
Commonly, plane strain conditions is called for, since this would cause minimum
toughness values to be obtained during the test. Such a toughness value is then
named a plane strain fracture toughness (K_{IC}).

Also, a further discrepancy exits
in terms of the stress solution far away from the crack tip, where the stresses
tend to disappear. This is obviously not true, since the stresses far away from
the crack should tend to have the magnitudes of the undisturbed stress field.
The complete stress field solution in fact has further terms:

_{} (3)

The
reason for only having considered the first, K dominated term, is that the
fracture process takes place in the region near to the crack tip where x is
small and the other terms are insignificant. Should the plastic zone become so
large that it engulfs the region dominated by the K-term, K will no longer
characterize the stress/strain state in the fracture process zone and can then
not be used as a fracture parameter.

**Elastic-plastic fracture
mechanics**

** **

In materials where the toughness
is large compared to the yield strength, LEFM will not apply. Elastic-Plastic
Fracture Mechanics (EPFM) has evolved as a non-linear extension of LEFM in an
energy formulation:

**LEFM **failurecriterion:
_{} (4)

Strain energy released by crack
extension:

_{} = energy required for crack extension. (5)

**EPFM **failurecriterion:
J = Hsea = J_{r } (6)

The
non-linear increase of strain with increasing stress during plasticity is then accounted
for. This failure criterion can then be applied when the plastic zone engulfs
the fracture process zone dominated by K.

The high
toughness materials usually dealt with in EPFM tend to display a rising
fracture toughness with crack extension (Jr does not remain constant after the
initiation of cracking). This phenomena, although not well understood, is
analogous to the strain hardening phenomena exhibited by some materials. This
implies that the fracture criterion may be expanded to an instability
criterion:

_{} (7)

_{} (8)

Such
an analysis can result in less conservative results than an initiation
analysis, since the reserve strength given by the rising fracture energy is
taken into account. It however requires that toughness data as a function of
stable crack growth needs to be determined. The analysis process followed is
dealt with later in this paper.

**EXPERIMENTAL METHODS**

** **

**LEFM
(K) fracture toughness testing**

An
ASTM and other similar standards have been established for plane strain
fracture toughness testing in terms of the K parameter [1]. The use of either
of two standard specimens is proposed, namely, a compact tension specimen (CT),
or a three-point bend specimen (TPB), as shown in Figure 1. The test method
involves fatigue pre-cracking from the machined notch (to ensure a sharp crack
front) and thereafter loading to failure whilst recording the load and the
load-line displacement. The crack length is measured after failure has
occurred.

From this data, a candidate fracture toughness is calculated, using the
load at what is said to be a nominal 0.2% crack extension (to ensure
unambiguous results), as well as the known geometry factors for these
specimens, which is then evaluated by testing its compliance to certain
validation requirements stipulated by the standard:

a) This requirement attempts to ensure that
plane strain conditions exist.

_{} (9)

b) This
avoids that a test be done on a specimen with an insignificant crack where the
failure would be by plastic collapse and not fracture.

_{} (10)

c) This requirement ensures that the plastic zone is sufficiently
small compared to the remaining ligament so as to ensure that the fracture
process zone is still dominated by the K-term.

_{} (11)

d) This requirement
limits the non-linearity of the load-displacement record, caused by stable
growth or plastic deformation.

**EPFM
(J) fracture toughness testing**

Standard
methods exist for the determination of the initiation toughness (J_{IC})
[2], as well as the rising fracture toughness in terms of J (the J_{r}
- curve) [3]. In essence, these material properties could be found from any
test on a specimen for which the geometry factors (b
and H) are known. The standard uses the same specimens described in the
previous section but unfortunately does not employ the now known
elastic-plastic geometry factors for these specimens, but rather an approximate
method, since at the time of establishing the standard these were not known.

Both
methods involve fracturing the specimen whilst measuring the crack extension,
as well as the load and loadline displacement. The measurement of crack
extension can be done using various methods. One such method, named the
unloading compliance method, involves partially unloading the specimen at
regular intervals during the ramping application of the fracture load, making
it possible to calculate the crack extension at each unloading event as a
function of the linear and decreasing unloading compliance. A typical test record
is shown in Figure 2.

The test results in a record of J as a function of
increments of crack extension (Da). For
the determination of the initiation toughness (J_{IC}) this R-curve is
then extrapolated back to zero crack growth (or rather to a blunting line to
take account of crack blunting without crack extension). The curve can also be
used as a J_{r} - curve for an instability analysis.

The
size requirements stipulated in the standards for ensuring plane strain conditions
is much less stringent than for the K_{IC} test, albeit that the J_{IC}**
**test standard claims that this initiation value can be converted to a
conservative K_{IC}** **value using the LEFM relationship.
This has been severely criticised by some authors [4], but the following
argument applies:

It
is argued that the thickness dependence of K_{IC} is due, not to the
thickness dependence of the initiation toughness, but rather to the thickness
dependence of the resistance curve, which comes into play because of the nominal
0.2% crack extension allowance inherent to the K_{IC }test procedure.
It is further argued that the true initiation toughness is almost independent
of thickness because even in relatively thin specimens, the initial, very
localized, crack extension takes place in plane strain. An explanation for this
is shown in Figure 3. The points marked (x) are points where instability occur.
For different thicknesses there are different R (or J_{r} ) curves,
therefore causing the observed trend of increasing toughness at 0.2% crack
extension for decreasing thicknesses. The stringent K_{IC} test size
requirements therefore are there to ensure that very little stable growth would
occur, to obtain a valid initiation toughness.

The J_{IC}** **test procedure circumpasses
these difficulties by extrapolating back to the true initiation toughness.

**INTERPRETATION OF TOUGHNESS DATA**

Figure 4 depicts a load
displacement record from a TPB specimen of a typical pressure vessel material.
This record shows the contribution towards displacement made by the elastic
deflection, plastic deflection and stable crack growth after initiation.

An EPFM initiation analysis on the
specimen is shown in Figure 5. This graph depicts the material J_{r}-curve
as a function of stable crack growth, as well as the crack driving force curves
in terms of J as a function of the crack length (a+Da).
The J_{tot}-curve shows that initiation has taken place at 38 kN. Also
shown is the J_{el}-curve (being equivalent to K) at this same load. Kc
= 8.5 MP(m)^{ 0.5} would have been determined from this test, which
would not have been a valid K_{IC} value.

Figure 6 depicts the
instability event at 48 kN.

If the toughness values are now to
be used to determine the failure load for a center cracked panel (CCP), the
following results would be obtained:

A LEFM initiation analysis using K_{C}
would result in a failure load of 310 kN. Figure 7 shows the true initiation
event determined from an EPFM analysis using J_{IC},** **which
results in a load of 260 kN. Figure 8 shows the instability event at a load of
290 kN.

From this example it is clear that
non-valid K_{C} results, or J_{IC}** **values converted to K_{IC},
used in a LEFM analysis, on a material that would exhibit significant
plasticity before fracture, would give un-conservative results.

Based on the above
arguments, the following guidelines can be given for the interpretation of
fracture toughness data for use in fracture analysis (r_{p} = plastic
zone size):

IF LEFM is applicable for the structure* *(r_{p}
<< W-a,a):

IF plane strain in the structure* *(r_{p}
<< B):

IF valid K_{IC} is available

Use
for initiation analysis (will be thickness and geometry independent)

ELSE

Use
J_{IC}** **to estimate K_{IC} (r_{p} << W-a,a
for test)

END

ELSE
(r_{p} » B in structure)

IF K_{r} or J_{r} curve is available

Use
in instability analysis (will thickness dependent)

ELSE

Use K_{C}
(will be geometry and thickness dependent)

END

END

ELSE (r_{p}
» W-a in structure)

IF plane
strain in structure* *(r_{p} < B)

Use J_{IC} for initiation

ELSE

IF J_{r}-curve is available

Use
for stability analysis (will be thickness dependent)

ELSE

Use Jc (will be geometry and
thickness dependent)

END

END

END