Daniela Scorza

A micro-mechanical model for statistically unidirectional and randomly distributed fibre-reinforced solids:

The use of reinforcing fibres in structural materials has been known since ancient time as an effective, simple and economic way to enhance their mechanical characteristics. Among the main mechanical properties that can be improved by such reinforcing techniques the tensile strength, the fracture and fatigue resistance, the wear resistance, the durability etc, can be referred. For the above-mentioned reasons, a tremendous effort in theoretical and experimental research on fibre-reinforced composite (FRC) materials has been made in order to develop suitable models capable of accurately describing the mechanical behaviour of such class of materials, at least at a macroscopic level. In the present paper, an energy-based homogenisation approach to model the mechanical behaviour of fibre-reinforced materials is developed by considering the possibility of fibre debonding and breaking, in order to obtain the macro constitutive equations. Furthermore, the effective spatial distribution of the fibres is accounted for by using its description in terms of probabilistic concepts; the case of randomly spatial-oriented fibres is also considered as a particular case by introducing a uniform probability distribution function. Some peculiarities of the model are outlined by discussing some simple examples in which the effects of different values of the involved parameters are considered.

Critical Plane Orientation Influence on Multiaxial High-Cycle Fatigue Assessment

In the present paper, the multiaxial fatigue lifetime of structural components failing in the high-cycle fatigue regime is evaluated by employing the modified Carpinteri-Spagnoli (C-S) multiaxial fatigue criterion based on the critical plane approach. In the above criterion, the critical plane position is linked to averaged principal stress directions through an off-angle 8. Then, the fatigue damage parameter used is determined by a nonlinear combination of an equivalent normal stress amplitude and the shear stress amplitude acting on the critical plane. In the present paper, some modifications of the original expression for the off-angle 8 are implemented in the modified Carpinteri-Spagnoli criterion. In particular, modified expressions recently proposed by Lagoda et al. are in accordance with the assumption originally developed by Carpinteri and co-workers, that is, the off-angle is a function of the ratio between the fatigue limit under fully reversed shear stress and that under fully reversed normal stress. Such expressions can be employed for metals ranging from mild to very hard fatigue behaviour. Some experimental data available in the literature are compared with the theoretical estimations and, only for materials with hard and very hard fatigue behaviour, the modified 8 relationships are shown to yield fatigue lifetime results slightly better than those determined through the original 8 expression.

Mechanics of interface debonding in fibre-reinforced materials

The evaluation of damage in multiphase materials plays a crucial role in their safety assessment under service mechanical actions. In this context, the quantification of the damage associated to fibre–matrix detachment is one of the most important aspects to be carried out for short fibre-reinforced materials. In the present article, the problem of progressive fibre–matrix debonding is examined and a mechanics interpretation of such a phenomenon is developed by relating the shear-lag and the fracture mechanics approach in order to determine the fibre–matrix interface characteristics. A multiscale approach is employed: at macroscopic level, composites with dilute dispersed fibres, arranged in a undirectional or in random orientation, are analysed through a homogenization approach, whereas the problem of axisymmetric debond growth in short fibres is examined at microscopic level. Moreover, a ‘structured’ linear elastic interface framework model for crack propagation analysis is applied by defining a microscopic truss structure, enabling to relate each other the classical shear strength approach and the fracture mechanics approach. Finally, a fibre pull-out test and some simple fibre-reinforced structural components are examined. This new proposed point of view on the debonding phenomenon allows a deep understanding of the mechanics of the fibre–matrix interface and enables to characterize such an interface layer that has a relevant role in mechanics design of composites materials.

Crack path dependence on inhomogeneities of material microstructure

Crack trajectories under different loading conditions and material microstructural features play an important role when the conditions of crack initiation and crack growth under fatigue loading have to be evaluated. Unavoidable inhomogeneities in the material microstructure tend to affect the crack propagation pattern, especially in the short crack regime. Several crack extension criteria have been proposed in the past decades to describe crack paths under mixed mode loading conditions. In the present paper, both the Sih criterion (maximum principal stress criterion) and the R-criterion (minimum extension of the core plastic zone) are adopted in order to predict the crack path at the microscopic scale level by taking into account microstress fluctuations due to material inhomogeneities. Even in the simple case of an elastic behaviour under uniaxial remote stress, microstress field is multiaxial and highly non-uniform. It is herein shown a strong dependence of the crack path on the material microstructure in the short crack regime, while the microstructure of the material does not influence the crack trajectory for relatively long cracks.

Joined application of a multiaxial critical plane criterion and a strain energy density criterion in low-cycle fatigue

In the present paper, the multiaxial fatigue life assessment of notched structural components is performed by employing a strain-based multiaxial fatigue criterion. Such a criterion, depending on the critical plane concept, is extended by implementing the control volume concept reated to the Strain Energy Density (SED) approach: a material point located at a certain distance from the notch tip is assumed to be the verification point where to perform the above assessment. Such a distance, measured along the notch bisector, is a function of both the biaxiality ratio (defined as the ratio between the applied shear stress amplitude and the normal stress amplitude) and the control volume radii under Mode I and Mode III. Once the position of the verification point is determined, the fatigue lifetime is assessed through an equivalent strain amplitude, acting on the critical plane, together with a unique material reference curve (i.e. the Manson-Coffin curve). Some uniaxial and multiaxial fatigue data related to V-notched round bars made of titanium grade 5 alloy (Ti-6Al-4V) are examined to validate the present criterion.

Fretting High-Cycle Fatigue Assessment through a Multiaxial Critical Plane-Based Criterion in Conjunction with the Taylor’s Point Method

The critical plane-based multiaxial criterion originally proposed by the authors for plain fatigue is here applied to estimate the crack initiation life of fretting high-cycle fatigued structural components. Although fretting fatigue can be regarded as a case of multiaxial fatigue, the common multiaxial fatigue criteria have to be modified to account for the severe stress gradients in the contact zone. Therefore, the above criterion is used in conjunction with the Taylor’s point method to numerically estimate the fatigue life of Ti-6Al-4V and Al-4Cu specimens under cylindrical contacts.

Mechanical Behaviour and Phase Transition Mechanisms of a Shape Memory Alloy by Means of a Novel Analytical Model

Abstract The aim of the present paper is to examine both the fatigue behaviour and the phase transition mechanisms of an equiatomic pseudo-elastic NiTi Shape Memory Alloy through cyclic tests (up to 100 loading cycles). More precisely, miniaturised dog-bone specimens are tested by using a customised testing machine and the contents of both austenite and martensite phase are experimentally measured by means of X-Ray diffraction (XRD) analyses. On the basis of such experimental results in terms of martensite content, an analytical model is here formulated to correlate the stress-strain relationship to the phase transition mechanisms. Finally, a validation of the present model by means of experimental data pertaining the stress-strain relationship is performed.

Investigation of Mode I fracture toughness of red Verona marble after thermal treatment

The present paper aims to assess the effect of freeze/thaw cycles on fracture behaviour of a natural stone: the red Verona marble. A wide variety of specimen types and methods to determine Mode I fracture toughness of natural stones are available in the literature and, in this context, the model originally proposed for plain concrete, i.e. the Two-Parameter Model (TPM), is adopted. Such a method is able to take into account the slow nonlinear crack growth occurring before the peak load, typical of quasi-brittle materials, with the advantage of easy specimen preparation and simple test configuration. In the present paper, the atmospheric ageing is simulated by means of thermal pre-treatments consisting of freeze/thaw cycles. Experimental tests are carried out using three-point bending Single-Edge Notched (SEN) specimens, according to the TPM procedure. The effects of thermal treatment on both mechanical and fracture parameters are examined in terms of elastic modulus and fracture toughness, respectively. KEYWORDS. Mode I Fracture Toughness; Red Verona Marble; Thermal Treatment; Two-Parameter Model.

Effect of fibre arrangement on the multiaxial fatigue of fibrous composites: a micromechanical computational model

Structural components made of fibre-reinforced materials are frequently used in engineering applications. Fibre-reinforced composites are multiphase materials, and complex mechanical phenomena take place at limit conditions but also during normal service situations, especially under fatigue loading, causing a progressive deterioration and damage. Under repeated loading, the degradation mainly occurs in the matrix material and at the fibre-matrix interface, and such a degradation has to be quantified for design structural assessment purposes. To this end, damage mechanics and fracture mechanics theories can be suitably applied to examine such a problem. Damage concepts can be applied to the matrix mechanical characteristics and, by adopting a 3-D mixed mode fracture description of the fibre-matrix detachment, fatigue fracture mechanics concepts can be used to determine the progressive fibre debonding responsible for the loss of load bearing capacity of the reinforcing phase. In the present paper, a micromechanical model is used to evaluate the unixial or multiaxial fatigue behaviour of structures with equi-oriented or randomly distributed fibres. The spatial fibre arrangement is taken into account through a statistical description of their orientation angles for which a Gaussian-like distribution is assumed, whereas the mechanical effect of the fibres on the composite is accounted for by a homogenization approach aimed at obtaining the macroscopic elastic constants of the material. The composite material behaves as an isotropic one for randomly distributed fibres, while it is transversally isotropic for unidirectional fibres. The fibre arrangement in the structural component influences the fatigue life with respect to the biaxiality ratio for multiaxial constant amplitude fatigue loading. One representative parametric example is discussed.