Polymethylmethacrylate Data from U-Notched Specimens and V-Notches with End Holes: A Synthesis by Means of Local Energy

2014 ◽  
Vol 627 ◽  
pp. 73-76
Author(s):  
A. Campagnolo ◽  
F. Berto ◽  
P. Lazzarin ◽  
M. Elices
Keyword(s):  
Strain Energy ◽  
Local Strain ◽  
Mean Value ◽  
Opening Angle ◽  
Static Loads ◽  
Large Variability ◽  
Notched Specimens ◽  
The Mean ◽  
Tip Radius ◽  
Notched Components

In this paper a volume criterion based on a simple scalar quantity, the mean value of the strain energy (SED), has been used to assess the static strength of notched components made of Polymethylmethacrylate (PMMA). The local-strain-energy based approach has been applied to a well-documented set of experimental data recently reported in the literature. Data refer to blunt U-notched cylindrical specimens of commercial PMMA subjected to static loads and characterised by a large variability of notch tip radius (from 0.67 mm to 2.20 mm). Critical loads obtained experimentally have been compared with the theoretical ones, estimated by keeping constant the mean value of the strain energy in a well-defined small size volume. In addition, some new tests dealing with V-notched specimens with end holes have been carried out to investigate the effect of the notch opening angle.

Static Multiaxial Fracture Behavior of Graphite Components: A Review of Recent Results

2017 ◽  
Vol 754 ◽  
pp. 35-38 ◽  
Author(s):  
S.M.J. Razavi ◽  
M. Peron ◽  
J. Torgersen ◽  
F. Berto
Keyword(s):  
Strain Energy Density ◽  
Strain Energy ◽  
Fracture Behavior ◽  
Local Strain ◽  
Opening Angle ◽  
Mode Mixity ◽  
Static Tests ◽  
Complete Set ◽  
Tip Radius ◽  
First Time

The problem of mixed mode (I+III) brittle fracture of polycrystalline graphite is investigated systematically here for the first time. The present study considers cylindrical specimens weakened by circumferential notches characterized by different acuities. A new complete set of experimental data is provided considering different geometrical configurations by varying the notch opening angle and the notch tip radius. The multiaxial static tests have been performed considering different values of the mode mixity ratio. A criterion based on the local Strain Energy Density previously applied by the same authors only to pure modes of loading is extended here to the case of tension and torsion loadings applied in combination.

On the Crack Initiated from the Bi-Material Notch Tip

2010 ◽  
Vol 452-453 ◽  
pp. 441-444 ◽  
Author(s):  
Tomáš Profant ◽  
Jan Klusák ◽  
Michal Kotoul
Keyword(s):  
Energy Density ◽  
Strain Energy Density ◽  
Strain Energy ◽  
Local Minimum ◽  
Plane Elasticity ◽  
Mean Value ◽  
Tangential Stresses ◽  
Density Factor ◽  
The Mean ◽  
Energy Density Factor

The bi-material notch composed of two orthotropic parts is considered. The radial and tangential stresses and strain energy density is expressed using the Stroh-Eshelby-Lekhnitskii formalism for the plane elasticity. The potential direction of the crack initiation is determined from the maximum mean value of the tangential stresses and local minimum of the mean value of the generalized strain energy density factor in both materials. Matched asymptotic procedure is used to derive the change of potential energy for the debonding crack and the crack initiated in the determined direction.

scholarly journals Interface-resolved simulations of particle suspensions in Newtonian, shear thinning and shear thickening carrier fluids

2018 ◽  
Vol 852 ◽  
pp. 329-357 ◽  
Author(s):  
Dhiya Alghalibi ◽  
Iman Lashgari ◽  
Luca Brandt ◽  
Sarah Hormozi
Keyword(s):  
Volume Fraction ◽  
Solid Volume Fraction ◽  
Shear Thickening ◽  
Fluid Phase ◽  
Local Strain ◽  
Reynolds Numbers ◽  
Mean Value ◽  
Strain Rates ◽  
Local Shear ◽  
The Mean

We present a numerical study of non-colloidal spherical and rigid particles suspended in Newtonian, shear thinning and shear thickening fluids employing an immersed boundary method. We consider a linear Couette configuration to explore a wide range of solid volume fractions ($0.1\leqslant \unicode[STIX]{x1D6F7}\leqslant 0.4$) and particle Reynolds numbers ($0.1\leqslant Re_{p}\leqslant 10$). We report the distribution of solid and fluid phase velocity and solid volume fraction and show that close to the boundaries inertial effects result in a significant slip velocity between the solid and fluid phase. The local solid volume fraction profiles indicate particle layering close to the walls, which increases with the nominal $\unicode[STIX]{x1D6F7}$. This feature is associated with the confinement effects. We calculate the probability density function of local strain rates and compare the latter’s mean value with the values estimated from the homogenisation theory of Chateau et al. (J. Rheol., vol. 52, 2008, pp. 489–506), indicating a reasonable agreement in the Stokesian regime. Both the mean value and standard deviation of the local strain rates increase primarily with the solid volume fraction and secondarily with the $Re_{p}$. The wide spectrum of the local shear rate and its dependency on $\unicode[STIX]{x1D6F7}$ and $Re_{p}$ point to the deficiencies of the mean value of the local shear rates in estimating the rheology of these non-colloidal complex suspensions. Finally, we show that in the presence of inertia, the effective viscosity of these non-colloidal suspensions deviates from that of Stokesian suspensions. We discuss how inertia affects the microstructure and provide a scaling argument to give a closure for the suspension shear stress for both Newtonian and power-law suspending fluids. The stress closure is valid for moderate particle Reynolds numbers, $O(Re_{p})\sim 10$.

Case Criterion of Crack Onset in Orthotropic Bi-Material Notches

2011 ◽  
Vol 465 ◽  
pp. 157-160 ◽  
Author(s):  
Tomáš Profant ◽  
Jan Klusák ◽  
Michal Kotoul
Keyword(s):  
Energy Density ◽  
Crack Initiation ◽  
Strain Energy Density ◽  
Strain Energy ◽  
Local Minimum ◽  
Plane Elasticity ◽  
Mean Value ◽  
Density Factor ◽  
The Mean ◽  
Energy Density Factor

A bi-material notch composed of two orthotropic parts is considered. The stresses and displacements are expressed using the Stroh-Eshelby-Lekhnitskii formalism for plane elasticity. The potential direction of crack initiation is determined from the maximum mean value of the tangential stress or the local minimum of the mean value of the generalized strain energy density factor in both materials [1, 2]. The matched asymptotic procedure is introduced to derive the change of potential energy for the debonding crack and the crack initiated in the determined direction [3].

scholarly journals Fatigue investigation of complex weldments by the means of the local strain energy density approach

2018 ◽  
Vol 165 ◽  
pp. 22003 ◽  
Author(s):  
Luigi Mario Viespoli ◽  
Antonio Alvaro ◽  
Bård Nyhus ◽  
Filippo Berto
Keyword(s):  
Fatigue Life ◽  
Energy Density ◽  
Welded Joints ◽  
Strain Energy Density ◽  
Strain Energy ◽  
Load Ratio ◽  
Local Strain ◽  
Opening Angle ◽  
Butt Weld ◽  
Numerical Predictions

The paper investigates the use of an energetic approach based on the strain energy density failure criteria to predict the fatigue life of welded joints in aluminum alloy. The cited criterion has already been proved valid to assess the failure of components in presence of sharp and blunt notches, and several results are present in the literature for different materials. The geometry tested in the present work is a double V-grooved full penetration butt weld, subsequently heat treated, and loaded orthogonally to the welding direction with load ratio R=0. This configuration makes the weld toe a notch of great opening angle. The aim of the paper is to verify the soundness of the energetic criteria for this class of welded joints, comparing the tests results with the numerical predictions. In the computational part, the energy in a given volume can be computed directly from the nodal displacements, thus not needing the stress values. Differently from the stress intensity factor approach, this property allows to a fast computation of the strain energy density by the means of a coarse mesh. The results of different configurations of geometry and meshing are compared to find the simplest modeling scheme capable of providing an accurate estimate of the fatigue life of the joint.

Effect of Carbon Black on the J-Integral and Strain Energy in the Crack Tip Region in a Vulcanized Natural Rubber

1987 ◽  
Vol 60 (5) ◽  
pp. 893-909 ◽  
Author(s):  
H. Liu ◽  
R. F. Lee ◽  
J. A. Donovan
Keyword(s):  
Energy Density ◽  
Carbon Black ◽  
Strain Energy ◽  
Process Zone ◽  
Crack Tip ◽  
Local Strain ◽  
Biaxial Stress ◽  
J Integral ◽  
Tearing Energy ◽  
Tip Radius

Abstract 1) The J-integral is path independent in both PS and SEN specimens and equals the tearing energy. 2) The critical J-integral at initiation is less in PS specimens than in SEN specimens, because the greater biaxial stress in PS restricts the process zone. 3) At initiation, the crack-tip radius, proportional to the local strain, is independent of CB. 4) The energy density within and the size of the process zone near the crack tip increase with CB; these are major contributions to CB reinforcement.

Variance of Fatigue Damage During Transportation

2018 ◽  
Author(s):  
Limin Yang ◽  
Tormod Bøe ◽  
Erik Falkenberg ◽  
Florus Korbijn
Keyword(s):  
Monte Carlo Simulation ◽  
Fatigue Damage ◽  
Offshore Structures ◽  
Mean Value ◽  
Scatter Diagram ◽  
Large Variability ◽  
Damage Prediction ◽  
Structural Fatigue ◽  
The Mean

Fatigue damage prediction of offshore structures during transportation is today commonly based on long term scatter diagram for the sea route. This gives a mean value for the expected fatigue. The deviation from the mean value may however be significant due to the large variability in metocean conditions for the typical short duration of the transport. The actual fatigue damage experienced during the voyage may therefore be much higher than predicted. Hence, it is recommended to take into account the variability of environmental conditions in the calculation of transportation fatigue. The aim of this paper is to establish a method for estimating transportation fatigue where the fatigue damage is computed with a specified level of non-exceedance. The fatigue damage is quantified by a measure as defined in OMAE2017 /1/. The distribution of this measure is obtained through Monte Carlo simulation of around 300 separate sea route scatter diagrams derived from hindcast data. The 90% percentile value (10% probability of exceedance) of the fatigue measure is then taken as target value and used for establishing a limited set of design fatigue sea states to be used in the structural fatigue damage calculations.

scholarly journals Local strain energy based fatigue assessment of cruciform welded joints: experimental data analysis and influence of hot-dip galvanization

2018 ◽  
Vol 188 ◽  
pp. 02013
Author(s):  
Luigi Mario Viespoli ◽  
Francesco Mutignani ◽  
Gabor Gulyas ◽  
Heikki Remes ◽  
Filippo Berto
Keyword(s):  
Structural Steel ◽  
Welded Joints ◽  
Strain Energy ◽  
Fatigue Testing ◽  
Computational Cost ◽  
Local Strain ◽  
Opening Angle ◽  
Fatigue Assessment ◽  
Significant Difference ◽  
Load Carrying

Performing the fatigue assessment of a welded joint using the Notch Stress Intensity Factors [1] presents two major challenges. The first is the necessity of a precise reconstruction of the stress field around the notch tip, thus needing an extremely refined discretization with an evident computational cost. The other, is that the dimensions of the N-SIFs and so their critical values, vary accordingly to the William’s solution [2] depending on the notch-opening angle. Consequence of this is that the mechanical properties necessary for the assessment vary as a function of the geometry treated. The research to overcome this issue has led to the use of the local Strain Energy Density [3]. The power of this parameter, used as a tool to perform fatigue assessment, consists of having a very low mesh refinement sensitivity [4], being the energy computed directly from nodal displacements and stiffness matrix [5], and having constant dimensions, so constant critical value for a given class of materials. In this paper, the local energetic method is applied to the analysis of the results of a series of tests performed on cruciform load carrying and non-load carrying specimens realized by S235 JRG2 structural steel plates. If load carrying, the fillet welded joints are made of S355 J2+N structural steel. The fatigue testing has been performed in atmosphere at room temperature in as welded condition both with and without the corrosion protective zinc layer. Particularly, the interest is focused on the influence of the zinc layer of the fatigue properties of the joint and on the capability of the local energetic approach, confronted with the classic nominal stress approach, to accurately predict the fatigue failure. To conclude, the investigation of the tests executed reveals no significant difference in the fatigue life for the coated samples, compared with the uncoated specimens and the predictions according to the IIW recommendations [6].

A Modified Strain-Energy Density Criterion Applied to Crack Propagation

1982 ◽  
Vol 49 (1) ◽  
pp. 81-86 ◽  
Author(s):  
P. S. Theocaris ◽  
N. P. Andrianopoulos
Keyword(s):  
Energy Density ◽  
Crack Initiation ◽  
Strain Energy Density ◽  
Strain Energy ◽  
Mean Value ◽  
Complex Functions ◽  
Slant Crack ◽  
Minimum Strain Energy ◽  
The Mean

An exact solution is presented to the problem of the crack-initiation direction by applying the minimum strain-energy density criterion in the case of a slant crack loaded uniaxially. The exact expressions of stresses, obtained from Muskhelishvili’s complex functions, are used in evaluating strain energy. Although the position of direction of the minimum density (ϑm) was accepted as the probable direction of the next kink of a propagating crack, the mean value of the strain-energy density is also introduced, instead of its minimum value, in the role of the critical quantity for crack initiation. Interesting results were derived for the behavior of this quantity concerning the phenomenon of bifurcation. The ratio of the mean-energy densities above and below the expected path of propagation is introduced as a second factor influencing the exact value of angle ϑm of propagation.

Sign in / Sign up

Export Citation Format

Share Document