Practical Application of a Geometrically Nonlinear Stress-Curvature Relation

1991 ◽  
Vol 239 ◽  
Author(s):  
Christine B. Masters ◽  
N. J. Salamon
Keyword(s):  
Strain Energy ◽  
Film Stress ◽  
Silicon Substrates ◽  
Substrate Thickness ◽  
Geometrically Nonlinear ◽  
Practical Application ◽  
Total Strain Energy ◽  
Initial Film ◽  
Nonlinear Stress ◽  
Film Substrate

ABSTRACTA recently developed geometrically nonlinear stress-curvature relation based on a minimization of the total strain energy, which predicts a bifurcation in shape as the magnitude of intrinsic film stress increases, is discussed in this paper. It is compared with the linear theories of Stoney and Brenner & Senderoff for a thin molybdenum film on silicon substrates with various thicknesses. Although the ratio of film to substrate elastic modulus is only 2, Stoney's equation generates significant error for this film/substrate system and the Brenner & Senderoff relation should be used for calculating initial film stress when plate deflections are small. When deflections exceed approximately half the substrate thickness the Brenner & Senderoff equation produces over 10% error and consequently, the nonlinear stress-deflection relation should be used to relate plate curvatures to initial film stress.

Geometrically Nonlinear Stress-Deflection Relations for Thin Film/Substrate Systems With a Finite Element Comparison

1994 ◽  
Vol 61 (4) ◽  
pp. 872-878 ◽  
Author(s):  
C. B. Masters ◽  
N. J. Salamon
Keyword(s):  
Thin Film ◽  
Finite Element ◽  
Ritz Method ◽  
Spherical Shape ◽  
Free Edge ◽  
Boundary Region ◽  
Film Stress ◽  
Geometrically Nonlinear ◽  
Nonlinear Stress ◽  
Film Substrate

A new higher order geometrically nonlinear relation is developed to relate the deflection of a thin film /substrate system to the intrinsic film stress when these deflections are larger than the thickness of the substrate. Using the Rayleigh-Ritz method, these nonlinear relations are developed by approximating the out-of-plane deflections by a second-order polynomial and midplane normal strains by sixthorder polynomials. Several plate deflection configurations arise in an isotropic system: at very low intrinsic film stresses, a single, stable, spherical plate configuration is predicted; as the intrinsic film stress increases, the solution bifurcates into one unstable spherical shape and two stable ellipsoidal shapes; in the limit as the intrinsic film stress approaches infinity, the ellipsoidal configurations develop into cylindrical plate curvatures about either one of the two axes. Curvatures predicted by this new relation are significantly more accurate than previous theories when compared to curvatures calculated from three-dimensional nonlinear finite element deflection results. Furthermore, the finite element results display significant transverse stresses in a small boundary region near the free edge.

Residual Stress Effects in the Scratch Adhesion Testing of Tantalum Thin Films

1993 ◽  
Vol 308 ◽  
Author(s):  
Richard L. White ◽  
John Nelson ◽  
William W. Gerberich
Keyword(s):  
Residual Stress ◽  
Critical Load ◽  
Failure Modes ◽  
Carbon Layer ◽  
Film Stress ◽  
Silicon Substrates ◽  
Percentage Decrease ◽  
Tantalum Films ◽  
Thin Carbon ◽  
Film Substrate

ABSTRACTThe effect of residual stress on the scratch adhesion critical load has been measured for sputtered tantalum films. In this single metallurgical system, six different failure modes could be observed, ranging from ductile ploughing to extensive spallation. For tantalum films deposited on silicon substrates, a 15% decrease in critical load was observed as the film residual stress increased from -1.1 GPa to +1.0 GPa. A larger percentage decrease (50%) was observed for films deposited on softer AIMg/NiP substrates. Film spallation was more extensive for films deposited over a thin carbon layer and for these films critical loads increased slightly with film stress. These results are substantially in contradiction with existing quantitative models for the scratch adhesion test and indicate that failure by shear at the film-substrate interface can be more important than failure by compressive buckling.

Microstructural evolution and piezoelectric properties of thick Pb(Zr,Ti)O3 films deposited by multi-sputtering method: Part I. Microstructural evolution

2007 ◽  
Vol 22 (5) ◽  
pp. 1367-1372 ◽  
Author(s):  
Chee-Sung Park ◽  
Jae-Wung Lee ◽  
Gun-Tae Park ◽  
Hyoun-Ee Kim ◽  
Jong-Jin Choi
Keyword(s):  
Grain Size ◽  
Microstructural Evolution ◽  
Strain Energy ◽  
Piezoelectric Properties ◽  
Columnar Structure ◽  
Thin Layers ◽  
Silicon Substrates ◽  
Si Substrate ◽  
Total Strain Energy ◽  
Pzt Films

Thick and crack-free Pb(Zr,Ti)O3 [PZT] films were fabricated on platinized silicon substrates by a multisputtering technique. The PZT films were deposited on the Si substrate by the radio frequency magnetron sputtering method using a single oxide target. As the film became thicker, its grain size increased. Therefore, the microstructure of the film was able to be controlled by repeatedly depositing thin layers. In addition, by using a seed layer with the same composition but a much smaller grain size, it was possible to further reduce the grain size of the film. When the film had a small in-plane grain size and a fibrous columnar structure, it was highly resistant to cracking, presumably because of its enhanced strength and structural stability. By exploiting these phenomena, highly dense, crack-free, and thick PZT films were successfully deposited up to a thickness of about 5 μm. The evolution of the crystallographic orientation of the film as a function of its thickness was also observed and correlated with the total strain energy of the system.

Energy Storage And Recovery In Thin Metal Films On Substrates

1997 ◽  
Vol 505 ◽  
Author(s):  
Shefford P Baker ◽  
Rose-Marie Keller ◽  
Eduard Arzt
Keyword(s):  
Plastic Deformation ◽  
Strain Energy ◽  
Dislocation Line ◽  
Line Length ◽  
Metal Films ◽  
Silicon Substrates ◽  
Cu Films ◽  
Compressive Flow ◽  
Film Substrate ◽  
Increasing Temperature

ABSTRACTDislocation segments which extend through the thickness of a film can move through the film only if dislocation line length is deposited or removed at the film/substrate and film/passivation (if any) interfaces. The dislocation density and, therefore, the energy stored in the film increase during plastic deformation. The reverse process, that is, the reduction of strain energy in the film by the reduction of dislocation line length, is here suggested to be the origin of a number of unexplained features of experimentally obtained stress-temperature curves, including very low (or even “negative”) yield stresses in compression, tensile-compressive flow stress asymmetries, increasing strength with increasing temperature upon heating, and a very strong Bauschinger-like effect which has been seen in thin Cu films. The results of stress-temperature measurements of passivated Cu thin films on silicon substrates are presented.

On the Stoney Formula for a Thin Film/Substrate System With Nonuniform Substrate Thickness

2007 ◽  
Vol 74 (6) ◽  
pp. 1276-1281 ◽  
Author(s):  
X. Feng ◽  
Y. Huang ◽  
A. J. Rosakis
Keyword(s):  
Thin Film ◽  
Misfit Strain ◽  
Film Stress ◽  
Substrate Thickness ◽  
Full Field ◽  
Temperature Changes ◽  
Thin Film Stress ◽  
Curvature Measurements ◽  
Film Substrate ◽  
Stoney Formula

Current methodologies used for the inference of thin film stress through system curvature measurements are strictly restricted to stress and curvature states which are assumed to remain uniform over the entire film/substrate system. Recently Huang, Rosakis, and co-workers [Acta Mech. Sinica, 21, pp. 362–370 (2005); J. Mech. Phys. Solids, 53, 2483–2500 (2005); Thin Solid Films, 515, pp. 2220–2229 (2006); J. Appl. Mech., in press; J. Mech. Mater. Struct., in press] established methods for the film/substrate system subject to nonuniform misfit strain and temperature changes. The film stresses were found to depend nonlocally on system curvatures (i.e., depend on the full-field curvatures). These methods, however, all assume uniform substrate thickness, which is sometimes violated in the thin film/substrate system. Using the perturbation analysis, we extend the methods to nonuniform substrate thickness for the thin film/substrate system subject to nonuniform misfit strain.

Parallel Glide: A Fundamentally Different Type of Dislocation Motion in Ultrathin Metal Films

2003 ◽  
Vol 779 ◽  
Author(s):  
T. John Balk ◽  
Gerhard Dehm ◽  
Eduard Arzt
Keyword(s):  
Thermal Cycling ◽  
Grain Boundaries ◽  
Film Surface ◽  
Metal Films ◽  
Geometric Constraints ◽  
Film Stress ◽  
Diffusional Creep ◽  
Creep Model ◽  
Substrate Interface ◽  
Film Substrate

AbstractWhen confronted by severe geometric constraints, dislocations may respond in unforeseen ways. One example of such unexpected behavior is parallel glide in unpassivated, ultrathin (200 nm and thinner) metal films. This involves the glide of dislocations parallel to and very near the film/substrate interface, following their emission from grain boundaries. In situ transmission electron microscopy reveals that this mechanism dominates the thermomechanical behavior of ultrathin, unpassivated copper films. However, according to Schmid's law, the biaxial film stress that evolves during thermal cycling does not generate a resolved shear stress parallel to the film/substrate interface and therefore should not drive such motion. Instead, it is proposed that the observed dislocations are generated as a result of atomic diffusion into the grain boundaries. This provides experimental support for the constrained diffusional creep model of Gao et al.[1], in which they described the diffusional exchange of atoms between the unpassivated film surface and grain boundaries at high temperatures, a process that can locally relax the film stress near those boundaries. In the grains where it is observed, parallel glide can account for the plastic strain generated within a film during thermal cycling. One feature of this mechanism at the nanoscale is that, as grain size decreases, eventually a single dislocation suffices to mediate plasticity in an entire grain during thermal cycling. Parallel glide is a new example of the interactions between dislocations and the surface/interface, which are likely to increase in importance during the persistent miniaturization of thin film geometries.

Fracture mechanics in design and service: ‘living with defects’ - Application of fracture mechanics to rubber articles, including tyres

1981 ◽  
Vol 299 (1446) ◽  
pp. 189-202 ◽  
Keyword(s):  
Fracture Mechanics ◽  
Crack Growth ◽  
Strain Energy ◽  
Tensile Failure ◽  
Practical Application ◽  
Complicated Fracture ◽  
Fracture Work

The use of a fracture mechanics approach, based on the rate of release of strain energy, to account for various features of the failure of vulcanized rubbers is outlined. The properties considered include those to which fracture mechanics is often applied — tear, tensile failure, crack growth and fatigue — and others to which its application is less usual — abrasion, ozone attack and cutting by sharp objects. The relation of macroscopically observed properties to the basic molecular strength of the material is also discussed. An example of a quantitative practical application of the rubber fracture work, to groove cracking in tyres, is then considered. Finally, the rather more complicated fracture that can occur in rubber—cord laminates is discussed and it is shown that the energetics approach can be applied to some features, at least, of this.

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