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**Context 1**

... the actual contact area of the surface is much smaller than the nominal contact area because of the roughness of the contact surfaces. According to Schaffrath’s model [1], the surface structure is characterized by pyramid units (Fig. 3). The following relation express can be obtained Combined with the force-deformation relation express, the relationship between pressure and contact area is showed in Fig. 10. The equipment used here is ZWICK Z050, which can be utilized for strain, shear and bending tests with different substrates and machine components with high accuracy of the cross head speed (0.0005- 2000 mm/min), position repetition accuracy (± 2 μ m) ...

**Context 2**

... is a composite made up of fibers, moisture, voids and chemical additives that are in the form of discrete fibers cross-linked in a complex network. The mechanical behavior of paper has a very close relationship with many operations in the printing production, such as printing, paper counting, folding, creasing, calendaring, cutting, etc. A number of studies have been made with the objective of predicting the stress-strain behavior of paper materials under the forces in MD and CD- directions, but the research in ZD-direction is limited. The purpose of this paper is to improve the mathematical model proposed by Schaffrath and extend the model to multiple sheets. Additionally, based on image processing technique, a new approach for measuring the actual contact area and calculating the relationship between force and actual contact area is presented. In the model proposed by Schaffrath [ 1, 2], who divided paper body into three parts, developed the models respectively and derived the force- deformation relationship of paper materials by using the Newton formula. Also, Stenberg [3, 4] published some articles between 2001 and 2003, in which he summarized the literature, developed a new device to measure the stress-strain properties of paperboard in ZD- direction, and built an elastic-plastic model for paper materials. The topography of paper surface could be measured today very precisely with different measurement methods, e. g., a NanoFocus μ SCAN system. For further processing, these physical data have to be transferred in an analysis model. As mentioned above, Stenberg and Schaffrath proposed mathematical models of paper materials in ZD-direction. Compared with the model proposed by Stenberg, the parameters needed in Schaffrath’s model are much easier to obtain. In this model, the paper body was divided into three parts: two surface structures and one internal structure, which can be described by using the following units (Fig. 3). After that Schaffrath built the models for the surface and internal structures. According to Hooke’s Law E F E A 0 x ...

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## Citations

... The influence of surface roughness was also discussed in some papers, for example, the paper surface topography under compression was studied by Teleman, et al. (2004). According to the surface topography, the paper body was considered as being composed of two rough surfaces and an internal structure (Schaffrath and Göttsching, 1991;Chen, Neumann and Dörsam, 2014), the force-deformation relationship of paper was derived by using the Newton formula. ...

The mechanical behavior of paper materials under compression in the out-of-plane direction is highly nonlinear. If the influence of the surface topography is not taken into account, the stress-strain curve of paper materials in the loading process is a typical example of materials with J-shaped compressive curves. When compression is released, the stress-strain curve in the unloading process is also nonlinear. The main purpose of this paper is to establish a suitable mathematical model and actualize the description of the compression curve for paper and paper stacks. The loading and unloading nonlinearities of paper stress-strain relations can be approximated by using different equations. In this paper, the loading curve of paper is calculated by using the sextic polynomial equation and the unloading curve is described by using the modified exponential function. All the used coefficients for determining the functions are expressed as the functions of the stress at the start point of unloading. The compressive behavior of paper under some given forces are also calculated by using the identified equation and verified by means of the experimental data. For multiple sheets, it is assumed that when the force is the same, the deformation of the paper stack is directly proportional to the number of sheets. Based on this assumption, the force-deformation relation of the paper stack is derived. The comparative analysis of the experimental results demonstrates the effectiveness of the description model.

... The method can be summarized as the following three steps [6]: Enlarging and transferring the pictures: the surface of the specimen is magnified 25 times under a binocular microscope and captured by a camera with pixels of 1200×1600. With the aid of MATLAB 8.1 [7], all pictures can be transferred into binary images. ...

The surface topography of paper can range from very rough to extremely smooth, which has significant influences on mechanical properties of paper materials, especially the compressive behavior of paper in the out-of-plane direction. Normally, the stress-strain relations of most of the materials are calculated by using the nominal contact area, which is the whole area of the pressure head. The difference between actual and nominal contact area is ignored, but they are very different, and cannot be neglected in all situations. In this paper, a new experimental method for evaluating the relationship between the actual contact area and the normal load is proposed. A carbon paper is introduced in this method, and it is assumed that the measured contact areas between carbon paper and the actually tested paper are the same as the actual contact areas between the pressure head and the tested paper. Based on this assumption, the mechanical behavior of paper in the out-of-plane direction could be discussed by calculating the actual stress-strain relation and deducing the actual modulus. In addition, the force sensitivities of different carbon papers used for showing the actual contact areas were also compared. The calculation results show the crucial differences between the actual and nominal stress-stain behaviors.

... In order to achieve high-yield and high-performing systems on paper, various efforts on characterizing paper at macro-, micro-and nanoscales abide ( [7], [8], [9]). Besides, new paper types are being fabricated to conform to specialized engineering applications. ...

Driven by low-cost, resource abundance and distinct material properties, the
use of paper in electronics, optics and fluidics is under investigation.
Considering sensor systems based on magneto-resistance principles (anisotropic,
giant, tunnel) that are conventionally manufactured onto inorganic
semiconductor materials, we propose the use of paper substrates for cost
reduction purposes primarily. In particular, we studied the magneto-resistance
sensitivity of permalloy (Py:Ni81Fe19) onto paper substrates. In this work, we
report on our findings with clean room paper (80 g/m2, Rrms = 2.877 {\mu}m, 23%
surface porosity, latex impregnation, no embossed macro-structure). Here, the
Py:Ni81Fe19 coating was manufactured by means of a dry process, sputter
deposition, and spans an area of 10x10 mm2 and a thickness of 70 nm. Employing
a four-point-probe DC resistivity measurement setup, we investigated the change
of electrical resistance of Py:Ni81Fe19 under the presence of an oriented
external magnetic field. In particular, we investigate the magneto-resistive
change at two configurations: (1) the direction of the magnetic field is
parallel to the nominal induced electric current and (2) the direction of the
magnetic field is perpendicular to the electric current. Due to the stochastic
orientation of the fibers interplaying with the Py:Ni81Fe19 coating, the change
in magneto-resistance of the overall system at both measurement configurations
closely corresponds to the classical response of Py:Ni81Fe19 at a +/-45{\deg}
angle between the direction of electrical current and magnetic field. Using the
magneto-optic kerr effect, we observed the formation of domain walls at the
fiber bending locations. Future work will focus on the impact of layer
thickness, fiber dimensions and structure of magnetic coating on the
performance of the paper-based Py:Ni81Fe19 magneto-resistors.