Putting iron alloys to the test.

As the trend to convert designs to cast components evolves, metalcasters must work with design engineers to discover which metal works best for each design and each application. In the automotive industry, fatigue properties are being examined for a number of metals, particularly the strain-life representation of iron alloys.

This representation has become a method of choice for structural design. Strain-controlled fatigue testing (as opposed to stress-life testing) focuses on the determination of fatigue behavior in the finite life regime. The resulting data is effective for computer aided design (CAD) modeling of fatigue behavior.

Although low-cycle fatigue properties are already available for many wrought alloys in the Society of Automotive Engineers (SAE) Fatigue Design Handbook and the SAE J1099 Information Report, a comprehensive strain-life database for cast iron did not exist to the public until recently. Although private industry has proprietary data, the AFS Cast Iron Division, with support from the U.S. Dept. of Energy Industrial Technology Office, addressed the issue using carefully specified castings from ASTM and SAE standard grades of irons.

In addition to strain-life testing, the castings were examined through chemical analysis, microstructure analysis, hardness tests, monotonic tension tests and compression tests. The result was a new database that extends CAD capabilities to cast irons. (The database can be purchased through the AFS.) This allows metalcasters to produce a casting for transportation with a different cost structure and elastic modulus to reduce fuel consumption yet maintain performance.

By working with design engineers, metalcasters can save time in labor by making single-piece components from products previously made of multiple castings.

Mediating Strain and Stress

Strain measurements are used routinely in experimental mechanics to monitor the stress environment at critical component locations. By knowing an alloy's stress-strain relationship the CAD software can be used to predict durability.

The strain-life data is generally acquired when the strain amplitude is the controlled variable during an axial fatigue test. Although the stress amplitude is not controlled, it's recorded during the fatigue test. The measured stress amplitude (at half-life) and the elastic modulus are used to separate the elastic and plastic components of the total strain for a linear-elastic material. The total strain-life technique is applicable to both high- and low-cycle fatigue problems. Experience with many materials has demonstrated that fatigue-life is related to both the elastic and plastic components of the total strain through simple power-law expressions (Fig. 1).

Fig. 1. These relationship are linear in log-log plots for both
elastic-strain vs. reversals and for plastic-strain vs. reversals.
This provides a simple means of determining the coefficients and
exponents to the power-law expressions. The total strain-reversal
curve is the sum of the two power-law expressions (inset).

POWER-LAW EXPRESSIONS FOR THE ELASTIC AND PLASTIC STRAIN

[DELTA][[epsilon].sub.e]/2 = [[sigma]'.sub.f]/E [(2[N.sub.f]).sup.b]
is the elastic strain amplitude.

[DELTA]/[[epsilon].sub.p]/2 = [[espilon]'.sub.f][(2[N.sub.f]).sup.c]
is the plastic strain amplitude.

Where 2[N.sub.f] is the reversals to failure (two reversals occurs
during each cycle) with four material constants:

[[sigma]'.sub.f] is the fatigue strength coefficient;

b is the fatigue strength exponent;

[[epsilon]'.sub.f] is the fatigue ductility coefficient;

c is the fatigue ductility exponent

[DELTA][epsilon]/2 = [[sigma]'.sub.f]/E[(2[N.sub.f]).sup.b]
+ [[epsilon]'.sub.f][(2[N.sub.f]).sup.c]

1 4 2 4 3   1 4 2 4 3
  elastic     plastic

As a material is subjected to cyclic loading, the stress-strain response changes. During strain-life testing, the cyclic stress-strain relationship is determined as well as coefficients and exponents for strain-life equations. In cyclic loading, the Ramberg-Osgood stress-strain relationship for the strain hardening exponent (n) and the strength coefficient (K) typically changes as the material hardens, or softens, until a stable state is reestablished. The stabilized values are referred to as the cyclic strain hardening exponent (n') and the cyclic strength coefficient (K'). The equation commonly used to obtain n' and K' from cyclic stress-strain hysteresis loops is:

[epsilon] = [[epsilon].sub.e] + [[epsilon].sub.p] = [sigma]/E + [([sigma]/K').sup.1/n],

In this expression E is the elastic modulus.

Together, the cyclic stress strain curve and the strain-life curve enable designers to account for local stress-strain conditions at stress concentrations like fillets. Moreover, modern CAD pack ages simulate the fatigue response to coincide with complex situations, such as random loading histories, load sequence effects and residual stresses.

All Iron Is Not Linear

The strain-life formalism assumes an initial linear elastic response that is symmetrical in tension and compression. The Ramberg-Osgood equation is based on linear elasticity and is implicit in both the strain-life relation and the cyclic stress-strain relation. However, gray irons exhibit a nonlinear stress-strain response, even at small strains; the "elastic" modulus varies nor only with the degree of strain, but with deformation history as well. Furthermore, the modulus is greater in compression than in tension. Consequently, it is impossible to separate the elastic and plastic components of strain on the basis of the "elastic" modulus, as described above.

An alternative treatment used for gray iron fatigue data is based on a simple linear logarithmic regression of the strain-life data according to the following relationship:

Log([N.sub.f]) = A + B x Log ([DELTA][epsilon]/2)

A and B are the strain-life constants.

The logarithm of total strain amplitude in Fig. 2 is not expected to vary linearly with the logarithm of fatigue life. However, for gray iron this happens because minimal plasticity occurs during fatigue. A log-linear method is ideal be cause it can be applied directly to the data generally published in the literature.

[FIGURE 2 OMITTED]

This log linear presentation of total strain-versus-fatigue life is analogous to a standard methodology employed for presenting stress life results. However, this method is less rigorous than the conventional strain-life formalism for linear-elastic materials, and some of the strain-life fatigue modeling capabilities ate sacrificed.

The presence of graphite also affects properties because it leads to initial nonlinear stress-strain responses in all types of graphitic cast iron. These effects vary with graphite morphology. They are most pronounced in gray iron, are generally negligible in ductile iron and are intermediate in compacted graphite iron. Since the compacted graphite iron graphitic morphology is a hybrid between gray iron and ductile iron, these results are reasonable. The nonlinear response of compacted graphite irons are neglected from a pragmatic point of view, and the conventional strain-life formalism can be used successfully.

Examine Your Options

The iron family of cast iron alloys: gray iron (and austenitic gray iron), ductile iron (and austenitic ductile iron), compacted iron, as well us the specialty wear resistant and elevated temperature irons provides the metalcasting community a broad spectrum of capability with favorable economics. The strain life fatigue data for 22 carefully specified and characterized grades of iron are available from an unbiased source. This provides the design community with the ammunition to seriously evaluate this overlooked diamond in the rough.

Information in this column was supplied by the AFS Cast Iron Division.