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Since spinal discs have a very poor blood supply, they also depend upon the circulation of joint fluids to bring in nutrients and expel waste. If a spinal joint loses its normal motion and this pumping action is impaired, the health of the disc deteriorates. Like a wet sponge, a healthy disc is flexible. A dry sponge is hard, stiff, and can crack easily.
Headaches are often caused when spinal nerves and the surrounding tissues become irritated or stretched. Initially, these nerves and blood vessels may become affected if the bones of the spine become misaligned or lose motion. Aspirin and other medications are available to dull headache pain, but they do not remedy the underlying cause - often spinal bones in the upper back and neck.Read More
It's believed that imbalances in the spinal structure often result from prolonged muscle strain, causing continuous tension on the discs, ligaments, muscles and bones. This tension is problematic, as it makes the back more susceptible to injury or re-injury. In general, any injuries to the spine may lead to various forms of lower back pain.
If the shoulder pops when rotating, and you begin hearing a popping noise when you move your shoulder, there could be many possible causes. As mentioned before, the joint is made up of a ball and socket, but more specifically, the humerus bone sits under and within the scapula, also known as the shoulder blade. These bones are all connected by four muscles, called the rotator cuff. Finally, cartilage, known as the labrum, helps hold the arm in place.
In some cases, the popping noise can be caused by osteochondroma. These are benign growths that develop in the shoulder, scapula, or rib cage. Due to these growths, cracking noises can occur when your arm is raised. More often than not, there are no other notable symptoms.
As we age over time, the soft cartilage that helps pad our bones degenerates, causing your bones to rub up against each other. This friction not only causes shoulder pain but cracking and popping noises when the shoulder joint is moved. In addition, the cracking and grating sound can also be an indication of arthritis.
Physical understanding of crack propagation is a fundamental issue in the industry. In the literature, crack velocities of polymer materials are strongly dependent on their visco-elastic properties and energy release rates. Recently, numerical and theoretical studies have proposed that structural sizes in polymers also influence on crack propagation. Here, using polymer sheets with similar visco-elastic properties but with different pore sizes, we vary explicitly the representative structural size and examine the effect of the size on crack propagation. Findings in this work help us to understand crack propagation in polymer materials and bio-inspired materials which have porous structures.
Physical understanding of crack propagation plays an essential role in the industry, and mechanical properties of materials with cracks have been studied for a wide range of materials such as metal, glass, and polymer. Recently, polymer materials attract considerable attention as a low-weight, tough, and inexpensive material for a new era. For example, recent polymer science has provided high toughness,[1] self-healing properties,[2] and high stretchablility[3,4] with polymer materials. The polymer is a prom-ising material, but an understanding of its fracture mechanism is still a challenging issue partially because both of its visco-elastic property and molecular-network structure are complex.
In the literature, crack behavior in polymer sheets has been studied with various methods, which include tensile,[5, 6] trou-ser,[7] cutting,[8] tearing,[9] and fixed-grip methods.[10] Most of the previous studies conclude that the energy for tearing a pol-ymer sheet correlates with the propagation velocity of a crack. Among these experimental methods, the fixed-grip method is a unique method to explore the behavior of crack propagation in polymer sheets. With this method, the so-called energy release rate G, which corresponds to tearing energy, takes a constant value during crack propagation, and the relationship between the energy release rate G and the crack-propagation velocity V can be clearly quantified. With the fixed-grip method, inter-esting characteristics of crack propagation on rubber sheets have been found: (1) power laws between energy release rate and crack velocity, and (2) a drastic velocity jump from a slow mode (1 mm/s) to a fast mode (1000mm/s) at a critical release rate.[10] The crack propagation under the fixed-grip con-dition has also been studied using the finite-element method, and the numerical results are qualitatively in accordance with experimental results.[11] More recently, an analytical theory reproduces the velocity jump, clarifying the physics of the jump.[12] Conventionally, the crack propagation in polymer sheets has been studied mainly based on their visco-elastic properties. Considering characteristic times[13] or rheological data,[14, 15] forms of crack tips and crack velocities are explained. On the contrary, recent works claim that crack mech-anism is also affected by the size of internal structures in poly-mer sheets. For example, by tuning a molecular weight of a cross-linking point of styrene-butadiene rubber, the relation between energy release rate versus tear rate is changed.[10] In the case of a polyethylene foam sheet whose typical foam size is of millimeter-scale, it was found that the flow of polymer happens only on the scale of foam at the crack tip.[16] The struc-tural size-effect is also verified with numerical simulations; it has been shown that, by changing the mesh size of a network model for elastic sheets, the failure stress of a sheet with a crack can be tuned.[17] For crack propagation, in a numerical simulation[18] and a theoretical model,[12] it is confirmed that mesh size affects crack velocities. In summary, recent works have implied that certain structural sizes of polymer sheets such as foam size and distance between cross-linking points, which correspond to the mesh size in theory and simulations, affect crack propagation and strength.
The importance of structural sizes in fracture of materials is not limited for polymer science. In Nature, biological soft/hard composites exhibit mechanical toughness (e.g., bones,[19,20] nacre[21] the exoskeleton of crustaceans[22,23]). Especially, soft bones of sea cucumbers,[24] the skeleton of a certain sponge,[25] and the frustule of diatoms[26] have void/material structures and can be regarded as ultimate soft/hard composites, in which voids play a role of soft elements. Accordingly, findings on crack propagation in porous media, which have void/material structures, help us to understand soft/hard composites in Nature and contribute to the development of bio-inspired tough materials.
In this work, we change explicitly the representative scale of structural size and study its effect on the relationship between energy release rate and crack-propagation velocity by using three types of porous polymer sheets: two polymer foam sheets (PFSs) and a nano-porous polymer sheet (NPS). All of the three sheets have similar visco-elastic properties, but the different crack behavior is observed in the experiment. Power laws between crack velocity and energy release rate are found for the two PFSs, while, for the NPS, crack propagation occurs only above a threshold value for energy release rate and the propagation velocity depends on energy release rate only weakly. Furthermore, our results share a common feature with previous experimental results obtained from rubber sheets, in terms of the size of internal structures. As a characteristic structural size (foam size and the distance between cross-linking point) increases, the exponent s of the power law between the energy release rate G andthe crackveloc-ity V (G Vs) increases. We present below experimental results and their physical interpretation.
Mechanical properties of matrix materials (i.e., cell walls and/or cell frames of each foam or pore in PFS and NPS) are relevant for elucidating crack behavior near the tip. However, in the present samples, the sizes of such matrix materials are minute, which is comparable with the size of a cellular struc-ture; cutting them out from samples and directly performing mechanical measurements on them are practically impossible. For this technical reason, we instead provide in this paper visco-elastic properties of the polymer sheets measured with rheometer by using stripes of dimension larger than the size of matrix materials, considering that it reflects physical proper-ties of the matrix materials. As visco-elastic properties contain characteristics concerning frequency, they are appropriate for discussing crack propagation.
In the present study, we examine a sheet with a porous struc-ture, for which we consider below the pore size is significantly important for considering crack propagation. In porous materi-als, physical properties such as crystallinity and glass-transition temperature of matrix materials can change with the size of pores. However, the direct measurement for matrix materials is impossible as explained above while these matrix properties are reflected in bulk viscoelastic measurements to some extent, which is similar for the three samples. In addition, the most important length scale at crack tips is the pore size; for example, the crack opening distance, the size of yielding zone near the crack tips,[28] the size of the region in which viscous flow occurs,[16] and the radius of curvature at a crack tip are all gov-erned by the pore size. These are the reasons we consider the pore size should be physically most important for considering crack propagation in the present porous polymers.
As shown in Fig. 2(a), both ends of a polymer sheet of initial length L is fixed with applying a fixed strain e. Once introduc-ing an initial crack at one of the two side edges, the elastic energy stored in the polymer sheet starts to be released to initiate crack propagation. Before introducing the initial crack, a stretch is manually applied to the sheet, and the stretch is fixed by a pair of clamping plates. This preparation for giving a pre-stretch before introducing the initial crack is completed within 30 min at room temperature around 25 C. Figure 2(b) presents the typical experimental result of crack propagation with the fixed-grip geometry (i.e. the relationship between crack length a and time). Except for an initial transient period of crack propagation (t < 50 s), the crack propagates at a con-stant speed. Here, we study the relationship between the con-stant crack velocity and the energy release rate for the three samples (PFSs and NPS). In the experiments, the maximum height of the sheet is set L to be either 200, 150, or 100 mm as indicated in the corresponding plots, while the width is set to be at least 2.5 times as large as L. In such a case, we can assume that the shape of a crack tip during crack propagation remains the same and thus energy release rate is constant. This constant can be represented by Se2L, where S is the shear modulus of the sheet, for small strains. Note that in the present experiments the maximum strains are relatively small: strains were applied up to ɛ = 18.5%, ɛ =28%, ɛ = 15% for PFS1, PFS2, and NPS, respectively. 153554b96e
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