Unusual nonlinear response of some metallic materials

Gil, Christopher M.; Lissenden, Cliff J.; Lerch, Bradley A.

doi:10.1016/s0167-6636(99)00018-6

Cited by 11 publications

(8 citation statements)

References 15 publications

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“…However, the orientation of the second longest axis of the lathes in the plane perpendicular to the longest axis cannot be determined accordingly. [1,19] In addition, identical tension and compression experiments were conducted with superimposed hydrostatic pressures of up to 630 MPa in order to determine if a pressure-dependent term The success could be attributed to the facts that the lattice mismatch in the two perpendicular directions on the (100) ␣ /(2 0) C common plane is very similar and the repeat distance along the two is close.…”

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confidence: 99%

“…Constitutive models for such materials will possess a pressure-dependent term that may arise from this volume expansion or internal friction-dependent deformation associated with non-Schmid effects at the crystal level. [1,19] In addition, identical tension and compression experiments were conducted with superimposed hydrostatic pressures of up to 630 MPa in order to determine if a pressure-dependent term [15] The present work was conducted in order to determine the magnitude of the SD effect at 298 K for two different aging conditions of IN 718, analogous to previous work.…”

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confidence: 99%

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Strength differential measurements in IN 718: Effects of superimposed pressure

Lewandowski

Wesseling

Prabhu³

et al. 2003

Metall Mater Trans A

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We realize that the 2.1 deg difference in orientation between the proposed and the Rong/Dunlop OR is small such that the latter might be derived by approximation due to a lack of detailed analysis at the atomic level. However, we cannot agree with the notion that the two are the same because the small angular difference can lead to large lattice strain at the interface with the M 2 C lathes having a finite width (ϳ20 nm, carbides "C" in Figure 2 [1] ), as observed in the present study.The comments on our article raised a good point in that the invariant line approach cannot explain the orientation of the longest axis of the M 2 C precipitates in ferrite. However, it fell short to elucidate the cause of the problem and to distinguish the two (lattice match and invariant line) methods in its argument. The invariant line method is based on the elastic continuum theory. Although the method relies on lattice mismatch data for its predictions, it disregards atomic (lattice point) match in its calculation. This can be readily understood by the fact that an invariant line derived in a lattice transformation is generally not required to coincide with the low-index lattice directions of both phases in question. As a result, it is often ineffective predicting particle orientations in coherent precipitation problems.For this reason, we did not resort to the invariant line approach for the prediction of the longest axis of the M 2 C carbides in our study. Instead, it was concluded that the small lattice mismatch and good atomic registration along the [100] ␣ /[2 0] C common direction controls the primary orientation of the carbide lathes. However, the orientation of the second longest axis of the lathes in the plane perpendicular to the longest axis cannot be determined accordingly. Our study indicated that the invariant line approach could give a satisfactory account of the orientation of the axis. The success could be attributed to the facts that the lattice mismatch in the two perpendicular directions on the (100) ␣ /(2 0) C common plane is very similar and the repeat distance along the two is close.It is understood that there are limitations to both the lattice match and invariant line approaches, [3] and neither could resolve all the orientation issues involved in the present problem alone. The lattice (atomic) match approach is expected to play a major role dominating precipitate orientations. The invariant line approach, on the other hand, becomes valid to the issue of the second axis of the M 2 C lathes when lattice match criterion fails to resolve. This latter orientation problem is nonexistent if the precipitates are viewed to be needle-shaped. Our experiments clearly showed, as well as others, [4,5,6] that the M 2 C carbides in these alloys were lath-shaped. Recent experiments on INCONEL* 718 (IN 718) indicate * INCONEL is a trademark of INCO Alloys International, Huntington, WV.that the yield and subsequent flow stress are significantly higher in compression than in tension [1] over a range of temperatures, exhib...

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confidence: 99%

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confidence: 99%

Strength differential measurements in IN 718: Effects of superimposed pressure

Lewandowski

Wesseling

Prabhu³

et al. 2003

Metall Mater Trans A

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“…Simulation of tests on the Inconel 718 thin-walled tubes subjected to torsion after tension or compression [12] The strength differential effect has been also observed by Gil et al [31,32] in the aged Inconel 718, a nickel base superalloy used Table 1 Material properties for the 2024-T351 aluminum alloy at room temperature. [12] are presented in Fig.…”

Section: Consistent Tangent Operatormentioning

confidence: 59%

Some applications of Burzyński yield condition in metal plasticity

2011

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a b s t r a c tThe classical J 2 plasticity theory is widely used to describe the plastic response of metallic materials. However, this theory does not provide satisfactory predictions for materials which exhibit pressure sen sitive yielding or plastic dilatancy. Another difficulty is the difference between the values of yield stresses in tension and compression for isotropic materials, the so called strength differential effect (SD), leading to the asymmetry of the elastic range. The Burzyń ski yield condition, proposed in 1928, can be used to overcome some of these problems. In this paper an implicit integration of the elasto plastic constitutive equations for the paraboloid case of Burzyń ski's yield condition is formulated. Also, the tangent operator consistent with the integration algorithm was developed and is presented. The proposed model was implemented in a commercial Finite Element code and different kinds of tests reported in the literature were simulated. The comparison between the numerical and experimental results shows that the plastic ity theory with the paraboloid case of Burzyń ski's yield condition describes adequately the strength dif ferential effect, which is present in many kinds of materials significant for recent applications.

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“…Thus, rather than truncate the strain energy function after the quadratic term, the cubic term is retained; resulting in hyperelastic constitutive equations where the stress-strain relationship is quadratic as given in Eqns. (2) and (17). Nevertheless, from the overall material response perspective shown in Figure 1 the response only deviates very slightly from linearity.…”

Section: Second Harmonic Generationmentioning

confidence: 91%

“…Clearly the model is not valid beyond the yield strength, where plastic deformation occurs. The material parameters for steel used in Figure 1 and throughout this paper are: The tensile and compressive stress-strain responses shown in Figure 1 are observed in the laboratory upon close examination 17 .…”

Section: Second Harmonic Generationmentioning

confidence: 99%

Cumulative second harmonics in weakly nonlinear plates and shells

2013

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The generation of cumulative second harmonic ultrasonic guided wave modes is analyzed with respect to their applications for nondestructive evaluation (NDE) and structural health monitoring (SHM). Due to the multimodal nature of guided waves, the selection of a primary wave mode that will generate a cumulative second harmonic is a critical first step for NDE and SHM applications. Thus, the nonlinear boundary value problem that must be solved by perturbation analysis is summarized and the results are tabulated for steel plates and circular cylindrical shells (pipes). The analysis includes shear-horizontal and Lamb waves in plates and axisymmetric torsional and longitudinal waves in pipes. Nonlinear finite element analyses that include kinematic and material nonlinearities are conducted for plate and pipe geometries. An excitation is applied to both plate and pipe samples by a simulated interdigitated transducer; SH1 for the plate and T(0,2) for the pipe. In each case a second harmonic mode having an orthogonal polarization is generated; S1 for the plate and L(0,4) for the pipe. In both cases the second harmonic grows linearly with propagation distance, and therefore is cumulative. A third example simulation is presented that demonstrates mode mixing in a pipe. T(0,3) and L(0,2) primary modes traveling in opposite directions intersect and generate significant harmonics at the sum and difference frequencies. Mode mixing provides a great opportunity to expand the potential of harmonic generation for NDE and SHM.

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Unusual nonlinear response of some metallic materials

Cited by 11 publications

References 15 publications

Strength differential measurements in IN 718: Effects of superimposed pressure

Strength differential measurements in IN 718: Effects of superimposed pressure

Some applications of Burzyński yield condition in metal plasticity

Cumulative second harmonics in weakly nonlinear plates and shells

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