Size Effect Law and Critical Distance Theories to Predict the Nominal Strength of Quasibrittle Structures

2013 ◽  
Vol 65 (2) ◽  
Author(s):  
Pere Maimí ◽  
Emilio V. González ◽  
Narcís Gascons ◽  
Lluís Ripoll
Keyword(s):  
Size Effect ◽  
Structural Strength ◽  
Critical Distance ◽  
Cohesive Law ◽  
Nominal Strength ◽  
Critical Fracture ◽  
Open Hole ◽  
Cracked Structures ◽  
Nonuniform Stress Field

The design of structures with a nonuniform stress field is of great industrial interest. The ability of the size effect law and critical distance theories to predict the nominal strength of notched and open hole specimens is analyzed in the present paper. The results obtained with these methods are compared with the solution of the problem computed, taking into account the material cohesive law. A conclusion of this paper is that the role of the critical fracture energy in determining the structural strength is negligible, except in large cracked structures. For unnotched structures of any size and for small cracked structures, the key parameter is the initial part of the softening cohesive law. This allows us to define design charts that relate the structural strength to a specimen size normalized with respect to a material characteristic length.

scholarly journals The role of the material fracture properties in the size-effect law of concrete structures

1996 ◽  
Vol 18 (1) ◽  
pp. 40-48
Author(s):  
V. Tran Tu
Keyword(s):  
Size Effect ◽  
Process Zone ◽  
Crack Opening ◽  
Concrete Structures ◽  
Fracture Propagation ◽  
Fracture Properties ◽  
Nominal Strength ◽  
Material Fracture ◽  
General Size

The size effect of the nominal stress at failure in concrete structures is dealt within general. An existence of a rather large fracture process zone in front of crack tip is proved to be the main reason leading to the size effect of the nominal strength. On the basis of the new general size-effect law and numerical results of fracture propagation, a particularly proposed size effect law for beams in bending is developed, in which the role of each material fracture characteristic, especially the shape of the stress - crack opening curve, is elaborated clearly.

An approximate analytical model for modification of size effect law for open-hole composite structure under biaxial load

2020 ◽  
pp. 095440622095937
Author(s):  
Mohammed Y Abdellah
Keyword(s):  
Size Effect ◽  
Composite Laminates ◽  
Approximate Model ◽  
Biaxial Stress ◽  
Damage Initiation ◽  
Main Challenge ◽  
Nominal Strength ◽  
Biaxial Stress State ◽  
Cohesive Laws ◽  
Open Hole

Nominal strength prediction remains the main challenge in the field of design and manufacturing of composite laminates. An approximate model to study the stress distribution around a circular hole in composite laminates is derived in this study. This model is constructed using well-known cohesive zone models and mainly depends on the un-notch strength and in-plane fracture toughness. The model attempts to modify and extend the specimen size effect curves, extracted using two-parameter cohesive laws (linear, exponential, and constant), into a biaxial stress state. It successfully predicts the damage initiation, propagation, and fracture of multidirectional composite laminates. Moreover, the stress concentration factor for a composite plate under varying biaxiality is calculated.

scholarly journals A Novel and Highly Effective Natural Vibration Modal Analysis to Predict Nominal Strength of Open Hole Glass Fiber Reinforced Polymer Composites Structure

Polymers ◽  
2021 ◽  
Vol 13 (8) ◽  
pp. 1251
Author(s):  
Mohammed Y. Abdellah ◽  
Mohamed K. Hassan ◽  
Ahmed F. Mohamed ◽  
Khalil Abdelrazek Khalil
Keyword(s):  
Size Effect ◽  
Modal Analysis ◽  
Composite Laminates ◽  
Fiber Reinforced Polymer ◽  
Reinforced Polymer ◽  
Glass Fiber Reinforced ◽  
Nominal Strength ◽  
Open Hole ◽  
Vibration Modal ◽  
Non Destructive

Glass fiber reinforced polymer (GFRP) composite laminates are considered the key material in many industries such as the infrastructure industries and the aerospace sector, and in building structures due to their superior specific strength and lightweight properties. The prediction of specimens’ nominal strength with open holes is still an attractive and questionable field of study. The specimen size effect is referred to its strength degradation due to the presence of holes when specimen geometry gets scaled. The non-destructive test used to measure the nominal strength of such material is a great tool for fast selection purposes, but not secure enough for several purposes. Furthermore, the destructive tests which are more expensive and time-consuming should be avoided in such structures. The present work aims to predict the nominal strength of open-hole GFRP’s composite using modal analysis of their natural frequency as non-destructive tests. At this end, the natural frequency, which is measured using modal analysis procedures, is combined with both linear elastic fracture mechanics (LEFM) and the theory of elasticity to predict the nominal strength of open-hole composite laminates. This advanced model employs two parameters of surface release energy resulting from a simple tension test and Young’s modulus based on vibration modal analysis. It is well established that these types of materials are also subjected to a size effect in dynamic response. Inversely to the known static loading size effect, the size effect in dynamic response increases with specimen size. The novel model gives excellent and acceptable results when compared with experimental and finite element ones. Size effects curves of a nominal strength of these laminates have a very close relative value with those obtained from finite element and analytical modeling. Moreover, the received design tables and graphs would be highly applicable when selecting suitable materials for similar industrial applications.

scholarly journals An Extended Finite Element Method (XFEM) Study on the Elastic T-Stress Evaluations for a Notch in a Pipe Steel Exposed to Internal Pressure

Mathematics ◽  
2021 ◽  
Vol 9 (5) ◽  
pp. 507
Author(s):  
K. Yakoubi ◽  
S. Montassir ◽  
Hassane Moustabchir ◽  
A. Elkhalfi ◽  
Catalin Iulian Pruncu ◽  
...  
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Internal Pressure ◽  
Extended Finite Element Method ◽  
Research Study ◽  
Extended Finite Element ◽  
T Stress ◽  
Cracked Structures ◽  
Element Method

The work investigates the importance of the K-T approach in the modelling of pressure cracked structures. T-stress is the constant in the second term of the Williams expression; it is often negligible, but recent literature has shown that there are cases where T-stress plays the role of opening the crack, also T-stress improves elastic modeling at the point of crack. In this research study, the most important effects of the T-stress are collected and analyzed. A numerical analysis was carried out by the extended finite element method (X-FEM) to analyze T-stress in an arc with external notch under internal pressure. The different stress method (SDM) is employed to calculate T-stress. Moreover, the influence of the geometry of the notch on the biaxiality is also examined. The biaxiality gave us a view on the initiation of the crack. The results are extended with a comparison to previous literature to validate the promising investigations.

scholarly journals Mechanics based statistical prediction of structure size and geometry effects on safety factors for composites and other quasibrittle materials

2008 ◽  
Vol 35 (1-3) ◽  
pp. 53-71 ◽  
Author(s):  
Zdeněk Bazant
Keyword(s):  
Mathematical Description ◽  
Structural Strength ◽  
Journal Article ◽  
Statistical Prediction ◽  
Probability Density Distribution ◽  
Safety Factors ◽  
Statistical Parameters ◽  
Size And Shape ◽  
Quasibrittle Materials ◽  
Nominal Strength

The objective of this paper1 is a rational determination of safety factors of quasibrittle structures, taking into account their size and shape. To this end, it is necessary to establish the probability density distribution function (pdf) of the structural strength. For perfectly ductile and perfectly brittle materials, the proper pdf's of the nominal strength of structure are known to be Gaussian and Weibullian, respectively, and are invariable with structure size and geometry. However, for quasibrittle materials, many of which came recently to the forefront of attention, the pdf has recently been shown to depend on structure size and geometry, varying gradually from Gaussian pdf with a remote Weibull tail at small sizes to a fully Weibull pdf at large sizes. This recent result is reviewed, and then mathematically extended in two ways: 1) to a mathematical description of structural lifetime as a function of applied (time-invariable) nominal stress, and 2) to a mathematical description of the statistical parameters of the pdf of structural strength as a function of structure size and shape. Experimental verification and calibration is relegated to a subsequent journal article.

scholarly journals Size Effect in Fracture of Sandwich Structure Components: Foam and Laminate

2001 ◽  
Author(s):  
Zdeněk P. Bažant ◽  
Yong Zhou ◽  
Drahomír Novák ◽  
Isaac M. Daniel
Keyword(s):  
Size Effect ◽  
Size Effects ◽  
Sandwich Structure ◽  
Maximum Load ◽  
Material Strength ◽  
Large Structures ◽  
Nominal Strength ◽  
Sandwich Plates And Shells ◽  
Extensive Test ◽  
Plates And Shells

Abstract In the design of sandwich plates and shells for very large structures, such as ships in the range of 100 m length, it is very important to take the size effect on the nominal strength into account, and do so in a realistic, physically justified, manner. Before the size effect is addressed for a sandwich structure, it must be understood for its components — the foam core and the laminate skins. In the current practice, the size effects are automatically attributed to the randomness of material strength, as described by the Weibull theory. The purpose of this paper is to show that in both the foam and the laminate there are deterministic size effects, which are generally more pronounced. They are caused by stress redistribution and energy release due to the growth of large fractures or large cracking zones prior to attaining the maximum load. This deterministic size effect is verified and calibrated by new tests of notched specimens of rigid close-cell vinyl foam. A combined deterministic-probabilistic theory of size effect of the laminates is proposed and verified by extensive test data.

Thickness-Dependent Tensile Behavior of Cu-Mn Alloys under Different Dislocation Slip Modes

2019 ◽  
Vol 294 ◽  
pp. 104-110 ◽  
Author(s):  
Le Le Kang ◽  
Dong Han ◽  
Xiao Wu Li
Keyword(s):  
Tensile Strength ◽  
Ultimate Tensile Strength ◽  
Size Effect ◽  
Uniform Elongation ◽  
Tensile Behavior ◽  
Dislocation Slip ◽  
Slip Mode ◽  
Planar Slip ◽  
Metallic Materials

To explore the role of dislocation slip mode playing in the size effect of mechanical behavior of metallic materials, the tensile behavior of Cu-5at.%Mn and Cu-20at.%Mn alloys with thickness (t) spanning from 0.1 to 2.0 mm is investigated. The results reveal that the yield strength σYS of Cu-5at.%Mn alloy displays an independence of thickness, whereas the ultimate tensile strength σUTS and the uniform elongation δ show an obvious size effect. The σUTS and δ first slightly decrease as t is reduced from 2.0 to 0.5 mm, but evidently drop when t is below 0.5 mm. A similar size effect is also exhibited in Cu-20at.%Mn alloy; however, the variation trend of “the smaller the weaker” in size effect can be weakened by the planar slip of dislocations occurring during the deformation of this alloy.

New Evidence on the Role of Size Effect in Determining the Pricing of Risk, Volatility Dynamics, and Economic Exposure of Firm Returns

2020 ◽  
Vol 9 (3) ◽  
pp. 1-25
Author(s):  
Faisal Khan ◽  
Sharif Ullah Jan
Keyword(s):  
Size Effect ◽  
Stock Returns ◽  
Firm Size ◽  
Research Study ◽  
Leverage Effect ◽  
Conditional Heteroskedasticity ◽  
Economic Factors ◽  
Monthly Data ◽  
New Evidence

This research study analyses the role of size effect in detecting the pricing of risk, various volatility dynamics, and economic exposure of firm returns on the Pakistani stock market by employing monthly data for the period from 1998 to 2018. Three generalized autoregressive conditional heteroskedasticity models were applied: GARCH(1,1) for capturing different volatility dynamics, GARCH-M for pricing of risk, and EGARCH for asymmetric and leverage effect. The findings of the study are as follows: Firstly, the authors untie that pricing of risk is subject to considerable variations with respect to firm size. Secondly, in the process of detecting whether the firm size matters in the case of asymmetry and leverage effect, they find that it is indeed the case. Thirdly, size effect plays a substantial role in determining various volatility dynamics. Finally, they uncover that economic factors affect stock returns differently based on firm size, signifying the role of size effect.

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