John M. Considine

Evaluation of strength-controlling defects in paper by stress concentration analyses

Cellulosic webs, such as paper materials, are composed of an interwoven, bonded network of cellulose fibers. Strength-controlling parameters in these webs are influenced by constituent fibers and method of processing and manufacture. Instead of estimating the effect on tensile strength of each processing/manufacturing variable, this study modifies and compares the point stress criteria and average stress criteria models used to estimate defect-free (i.e., maximum possible) tensile strength and the inherent size of the cumulative effect of strength-limiting defects. The two major modifications to these models were to assume that defect-free tensile strength was unknown and that unnotched tensile strength was reduced by the presence of inherent defects. These modifications allow the calculation of inherent defect size and defect-free tensile strength by characterizing the tensile strength of the web in the presence of stress concentrations associated with holes of different radius. The models were applied to seven paper materials including lightweight, commercial papers, linerboards, and cylinder boards; estimated inherent defect sizes ranged from 0.1 to 1.5 mm. For most materials considered, defect size was larger in the 2-direction than the 1-direction. Actual measured tensile strengths ranged from 59% to over 95% of the estimated defect-free tensile strengths, σu.

Effect of Inorganic Fillers in Paper on the Adhesion of Pressure-Sensitive Adhesives

Inorganic fillers are inexpensive materials used to increase the density, smoothness and other properties of paper that are important for printing. In the current study, the adhesion of pressure-sensitive adhesives (PSAs), a common type of adhesive used in labels and tapes, to papers containing varying amounts and types of fillers is investigated. Papers with three types of fillers, precipitated calcium carbonate (PCC), ground calcium carbonate (GCC) and kaolin clay, were investigated. The compositions of the papers were examined with SEM/EDX, while peel and double cantilever beam (DCB) tests were used to assess PSA–paper adhesion. The results indicate that fillers enhance the adhesion between PSA and paper. In the case of the peel tests, a combination of inter-fiber bond strength and PSA–paper adhesion determines the peel strength. While in the DCB tests, failure is isolated to the PSA–paper interface, thus allowing measurements of pure interfacial failure.

Improved Instrumented Indentation of Soft Materials through Surface Deformation Measurements

Instrumented indentation is a commonly used technique to determine the mechanical properties of bulk materials and thin films by measuring the load and displacement during indentation into a specimen. However, in traditional indentation measurements, it can often be difficult to determine the true deformation of the specimen due to the machine compliance and drift in the system. The issue of drift is particularly problematic in tests that occur over extended time scales, such as creep tests on soft materials. In the present work, a new method, in which the full-field deformation of the sample material around the indenter is measured, is presented to overcome these challenges. Specifically, the deformation of specimens during cylindrical flat punch indentation tests is monitored by tracking discrete particles, such as microbeads, near the surface of the sample. This method allows for direct measurement of the specimen surface as it is deformed. In the current implementation, it is applicable to transparent materials, including many polymers, gels, and biological materials. An inverse method was developed to extract mechanical properties of the specimen from the measured displacement fields. A numerical parametric study was performed to quantify the effect of changes in Poisson’s ratio, magnification, particle density, and experimental noise on the elastic properties calculated using the inverse method.

An Inverse Method for Analyzing Defects in Heterogeneous Materials

Evaluation of defects in heterogeneous materials, such as cellulose-fiber composites, can lead to methods for improving strength. Full-field displacement measurement techniques, e.g., digital image correlation and electronic speckle pattern interferometry, provide useful information by which defects can be evaluated. Inverse Methods (IM) have been used to determine material properties from full-field displacement data. In homogenous materials, the resulting system of equations relating displacements with applied load and constitutive properties is overdetermined and is solved with traditional least squares methods. However, heterogeneous materials create an underdetermined system that cannot be addressed in the same way. Numerically simulated heterogeneous, orthotropic materials were evaluated in a 2-D finite element model, and the resulting nodal displacements were used as input to an IM algorithm. The algorithm determined local moduli, Ex and Ey, with errors, ranging from 9% to 20%. Errors in calculated Gxy were greater. Techniques for reducing error are provided. Simulations suggested IM can be an important tool in defect evaluation given full-field displacement measurements.

Determination of Constitutive Properties in Inverse Problem Using Airy Stress Function

A new inverse problem formulation is developed using the Airy stress function. Inverse methods are used to determine the constitutive properties of a graphite/epoxy laminated composite loaded vertically by processing measured values of v-displacement component with an Airy stress function in complex variables. Displacements are recorded using digital image correlation. The traction-free conditions on the symmetrically located sided notches are satisfied analytically using conformal mappings and analytic continuation. The traction-free on the vertical free edge and a symmetrical condition on horizontal line of symmetry are imposed discretely. The primary advantage of this new formulation is the direct use of displacement data, eliminating the need for numerical differentiation when strain data is required. The inverse method algorithm determined the constitutive properties with errors range from 2% to 10%. Selection of Airy coefficients, test geometry configuration and comparison with other inverse methods will be addressed.

Measuring the Elastic Modulus of Soft Thin Films on Substrates

The use of instrumented indentation to measure the mechanical properties of thin films supported on substrates where the Youngs modulus of the film (E1) is substantially less than that of the Youngs modulus of the substrate (E2) with modulus ratios from E1/E2 = 0.0001 to 1 is important for investigating materials such as soft polymers, cellulosic sheets, and biological materials. Most existing models for determining the elastic properties of films or sheets on substrates from indentation measurements were developed for the analysis of metal and dielectric films on semiconductor substrates and thus have been used in cases where E1/E2 is ~0.01 to ~10. In the present work, flat punch indentation of systems with E1/E2 = 0.0001 to 1 is investigated via finite element (FE) modeling and experiments. A FE parametric study in which E1/E2 was varied from 0.0001 to 1 was performed to quantify the effect of substrate stiffness on the measurement of the elastic film properties. A semi-analytical model that treats the thin film and substrate as two springs in series was fit to the FE results to allow for use of the results presented. Preliminary experiments, in which a series of film/substrate systems with various modulus mismatch (E1/E2 from ~0.0005 to ~1) were characterized using instrumented indentation, were performed to evaluate the effectiveness of the model for extracting films properties from indentation measurements. The results of the parametric FE study show that for very stiff substrates, the measured stiffness becomes insensitive to changes in substrate modulus. The analytical model and FE model agree to within 7% for E1/E2 values between 0.0001 to 1 and a/t ratios from 1 to 100. Comparison of the preliminary experimental results and FE model show reasonable agreement, but further investigation is required to obtain better correlation.

Mechanical Characterization of Cellulose Nanofibril Materials Made by Additive Manufacturing

Cellulose nanomaterials have high specific stiffness and strength, are optically transparent, and are biodegradable, making them an attractive building block for bulk materials. The overall dimensions of neat bulk cellulose nanofibril (CNF) materials is significantly limited by the development of residual stresses generated during the drying process, when the source CNF is 1.0 wt.% in water or less, or by agglomeration, when the source CNF is greater than 1.0 wt.%. Here, we overcome these issues by producing CNF films and structures by additive manufacturing (i.e., 3D printing) of a shear thinning aqueous CNF suspension onto hydrophobic substrates under controlled drying conditions. Films of enhanced thicknesses, greater than 80 μm, are achieved as a result of the multistep layer-by-layer manufacturing process. The mechanical properties of the resulting materials are characterized via nanoindentation and tensile testing. Nanoindentation is used primarily to map the mechanical properties and examine variations in properties spatially and through the thickness. Tensile testing, with strain measurement via digital image correlation, is used to characterize the bulk properties. Mechanical characterization is supported by additional characterization via atomic force, optical, and electron microscopy. This study demonstrates the ability to additively manufacture stiff, strong, uniform, and scalable cellulose nanofibril materials.

Determination of Constitutive Parameters in Inverse Problem Using Thermoelastic Data

A new inverse problem formulation for identification of constitutive parameters in orthotropic materials from load-induced thermal information is developed using Levenberg-Marquardt Algorithm and Airy stress function. Inverse methods were used to determine the constitutive properties as well as the thermoelastic calibration factors of a loaded perforated graphite/epoxy laminated composite by processing noisy simulated thermoelastic data with an Airy stress function in complex variables. Equilibrium, compatibility, and traction-free condition on the boundary of the circular hole are satisfied using complex-variable formulation, conformal mapping and analytic continuation. The primary advantage of this new formulation is the direct use of load-induced thermal data to determine the constitutive parameters, separate the stresses, i.e., evaluate the individual stress components, including on the edge of the hole, and smooth the measured data, all from a single test. The inverse method algorithm determined the constitutive properties with errors less than 10%.

Use of Bulge Test Geometry for Material Property Identification

The bulge test geometry, sometimes called blister or burst test, has a long history of use for material property identification. Paper materials are thin with relatively low stiffness; in a bulge test paper materials will exhibit a combination of membrane and plate behavior. We have developed a VFM examination to identify the in-plane stiffnesses of this type of material by incorporating both membrane and plate internal work.

Optimized Test Design for Identification of the Variation of Elastic Stiffness Properties of Loblolly Pine ( Pinus taeda ) Pith to Bark

This article presents the design optimization of an un-notched Iosipescu test specimen whose goal is the characterization of the material elastic stiffnesses of a Loblolly (Pinus taeda) or Lodgepole pine (Pinus contorta) sample in one single test. A series of finite element (FE) and grid simulations were conducted to determine displacement and strain fields for various ring angles, ring spaces, and proportions of latewood per ring. These displacement and strain fields were utilized to determine the constitutive parameters for the woody material using VFM. Using an error function based on a comparison of the input stiffnesses and those identified by grid simulation information it was possible to narrow the optimum ring angle at which test specimens should be tested. The results of this work suggest that the starting angles for the un-notched Iosipescu test specimens should be approximately 45° to produce the smallest identification error.