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IN THIS ISSUE

### Research Papers

J. Appl. Mech. 2017;85(2):021001-021001-11. doi:10.1115/1.4038424.

Buckled drillstring easily existed in extended-reach drilling (ERD) engineering, causing casing wear more severe. However, the effect of the buckled drillstring on casing wear prediction is going unheeded in long-term studies. To solve the issue, this paper proposes a new model, named as circumferential casing wear depth (CCWD) model, based on the energy principle and the more complicated geometry relationship than that in casing wear groove depth (CWGD) model. Meanwhile, sensitivity analysis of parameters clearly describes the changing trends among them. With the established composite wear models, the change of casing wear depth versus drilling footage under different composite wear cases is also discussed. The results show that the severe casing wear may occur if there is the buckled drillstring; due to the greater contact force and more sophisticated wear shape than those under nonbuckling condition, a shorter drilling footage could make a larger calculation error when only CWGD model is used. In the case study, the method of the inversion of casing wear factor from the drilled well can be used to predict the well whose structure resembles it; the revised coefficient, the maximum risky casing wear depth can be evaluated for each wellbore section to avoid drilling engineering failure. The new model provides a practical method to improve the prediction accuracy of casing wear in ERD. Neglecting the effect of the buckled drillstring will make the prediction underestimated and a great economic loss, which is significant for ERD.

Topics: Wear , Drill strings
Commentary by Dr. Valentin Fuster
J. Appl. Mech. 2017;85(2):021002-021002-7. doi:10.1115/1.4038497.

Temperature-sensitive hydrogel is blessed with outstanding properties which may be utilized for innovative appliance. However, this is not achievable if the phase transition property of it is not well understood. Under certain mechanical constraint or temperature stimuli, the hydrogel shows the phase transition, a very special phenomenon that has been study for decades. Those studies have cumulated many qualitative conclusions, yet the quantitative ones are still evasive. Using dynamic mechanical analysis (DMA), we have conducted experiments to quantitatively investigate this peculiar behavior. It is evident that the higher the temperature stimuli applied to hydrogel, the higher the stress which triggers phase transition. Based on the experimental results, a decision rule which predicts the stress triggering phase transition is proposed. Furthermore, theoretical study has also been carried out to study this phase transition phenomenon. With a proper fitting parameter and a transformation from referential state to free swelling state, we can compare the theoretical prediction of the stress–stretch curve with results from experiments. Besides experimental observations and theoretical analyses, another feature of this paper is to provide a numerical method to study phase transition under mechanical constraints.

Commentary by Dr. Valentin Fuster
J. Appl. Mech. 2017;85(2):021003-021003-12. doi:10.1115/1.4038496.

This paper investigates the effect of strain rate on the scaling behavior of dynamic tensile strength of quasibrittle structures. The theoretical framework is anchored by a rate-dependent finite weakest link model. The model involves a rate-dependent length scale, which captures the transition from localized damage to diffused damage with an increasing strain rate. As a result, the model predicts a rate- and size-dependent probability distribution function of the nominal tensile strength. The transitional behavior of the strength distribution directly leads to the rate and size effects on the mean and standard deviation of the tensile strength. The model is verified by a series of stochastic discrete element simulations of dynamic fracture of aluminum nitride specimens. The simulations involve a set of geometrically similar specimens of various sizes subjected to a number of different strain rates. Both random microstructure geometry and fracture properties are considered in these simulations. The simulated damage pattern indicates that an increase in the strain rate results in a more diffusive cracking pattern, which supports the theoretical formulation. The simulated rate and size effects on the mean and standard deviation of the nominal tensile strength agree well with the predictions by the rate-dependent finite weakest link model.

Commentary by Dr. Valentin Fuster
J. Appl. Mech. 2017;85(2):021004-021004-8. doi:10.1115/1.4038610.

An efficient and novel micromechanical computational platform for progressive failure analysis of fiber-reinforced composites is presented. The numerical framework is based on a recently developed micromechanical platform built using a class of refined beam models called Carrera unified formulation (CUF), a generalized hierarchical formulation which yields a refined structural theory via variable kinematic description. The crack band theory is implemented in the framework to capture the damage propagation within the constituents of composite materials. The initiation and orientation of the crack band in the matrix are determined using the maximum principal stress state and the traction-separation law governing the crack band growth is related to the fracture toughness of the matrix. A representative volume element (RVE) containing randomly distributed fibers is modeled using the component-wise (CW) approach, an extension of CUF beam model based on Lagrange type polynomials. The efficiency of the proposed numerical framework is achieved through the ability of the CUF models to provide accurate three-dimensional (3D) displacement and stress fields at a reduced computational cost. The numerical results are compared against experimental data available in the literature and an analogous 3D finite element model with the same constitutive crack band model. The applicability of CUF beam models as a novel micromechanical platform for progressive failure analysis as well as the multifold efficiency of CUF models in terms of CPU time are highlighted.

Commentary by Dr. Valentin Fuster
J. Appl. Mech. 2017;85(2):021005-021005-7. doi:10.1115/1.4038640.

This investigation considers the dynamic stability of the steady-state frictional sliding of a finite-thickness elastic layer pressed against a moving rigid and flat surface of infinite extent. The elastic layer is fixed on its bottom surface; on its entire top surface, the rigid surface slides with constant speed and with a constant friction coefficient. The plane-strain equations of motion for a linear isotropic elastic solid are solved analytically for small dynamic disturbances. The analysis shows that even with a constant (speed-independent) friction coefficient, the steady solution is dynamically unstable for any finite friction coefficient. Eigenvalues with positive real parts lead to self-excited vibrations which occur for any sliding speed and which increase with increasing coefficient of friction. This is in contrast to the behavior of an elastic half-space sliding against a rigid surface in which the instability only occurs if the coefficient of friction is greater than unity. This work and its extensions are expected to be relevant in the theoretical aspects of sliding friction as well as in a variety of areas such as earthquake motion and brake dynamics.

Commentary by Dr. Valentin Fuster
J. Appl. Mech. 2017;85(2):021006-021006-9. doi:10.1115/1.4038683.

The control of geometric shapes is well acknowledged as one of the facile routes to regulate properties of graphene. Here, we conduct a theoretical study on the evaporation-driven self-folding of a single piece of graphene nanoribbon that is immersed inside a liquid droplet prior, and demonstrate the folded pattern, which is significantly affected by the surface wettability gradient of the graphene nanoribbon. On the basis of energy competition among elastic bending deformation, liquid–graphene interaction and van der Waals force interaction of folded nanoribbons, we propose a theoretical mechanics model to quantitatively probe the relationship among self-folding, surface wettability gradient, and pattern and size of ultimate folded graphene. Full-scale molecular dynamics (MD) simulations are performed to validate the energy competition and the self-folded patterns, and the results show good agreement with theoretical analyses. This study sheds novel insight on folding graphene nanoribbons by leveraging surface wettability and will serve as a theoretical guidance for the controllable shape design of graphene nanoribbons.

Commentary by Dr. Valentin Fuster
J. Appl. Mech. 2017;85(2):021007-021007-12. doi:10.1115/1.4038698.

Swelling and crack propagation in ionized hydrogels plays an important role in industry application of personal care and biotechnology. Unlike nonionized hydrogel, ionized hydrogel swells up to strain of many 1000's %. In this paper, we present a swelling driven fracture model for ionized hydrogel in large deformation. Flow of fluid within the crack, within the medium, and between the crack and the medium are accounted for. The partition of unity method is used to describe the discontinuous displacement field and chemical potential field, respectively. In order to capture the chemical potential gradient between the gel and the crack, an enhanced local pressure (ELP) model is adopted. The capacity of this numerical model to study the fracture and swelling behaviors of ionized gels with low Young's modulus (< 1 MPa) and low permeability (< 10−16 m4/Ns) is demonstrated. Two numerical examples show the performance of the implemented model (1) swelling with crack opening and (2) swelling with crack propagation. Simulations demonstrate that shrinking of a gel results in decreasing macroscopic stress and simultaneously increasing stress at crack tips. Different scales yield opposite responses, underscoring the need for multiscale modelling. While cracking as a result of external loading can be prevented by reducing the overall stress level in the structure, reducing overall stress levels will not result in reducing the crack initiation and propagation due to swelling.

Commentary by Dr. Valentin Fuster

### Technical Brief

J. Appl. Mech. 2017;85(2):024501-024501-6. doi:10.1115/1.4038495.

The indentation of flat surfaces deforming in the plastic regime by various geometries has been well studied. However, there is relatively little work investigating cylinders indenting plastically deforming surfaces. This work presents a simple solution to a cylindrical rigid frictionless punch indenting a half-space considering only perfectly plastic deformation. This is achieved using an adjusted slip line theory. In addition, volume conservation, pileup and sink-in are neglected, but the model can be corrected to account for it. The results agree very well with elastic-plastic finite element predictions for an example using typical steel properties. The agreement does diminish for very large deformations but is still within 5% at a contact radius to cylinder radius ratio of 0.78. A method to account for strain hardening is also proposed by using an effective yield strength.

Commentary by Dr. Valentin Fuster

### Errata

J. Appl. Mech. 2017;85(2):027001-027001-2. doi:10.1115/1.4038611.

This erratum concerns the replacement of expressions (39)(42) in the original article by the expressions listed below: Display Formula

(39)$M=(p0s00p0−ss0−t00−s0−t)$
Display Formula
(40)$E=(1/20s/2p001/20−s/2p−s/2t01/200s/2t01/2)$
Display Formula
(41)$M¯=(p¯10s¯100p¯20−s¯2s¯30−t¯100−s¯40−t¯2)$
Display Formula
(42)$p¯p=(1−V12)(σ+1)(1−V1)2σ+(1+V1)2, s¯s=(1−V1)2(σ+1)(1−V1)2σ+(1+V1)2, t¯t=(1−V12)(σ+1)(1−V1)2σ+(1+V1)2$

Commentary by Dr. Valentin Fuster