Solid Creep Research Articles

Editorial of the 1st Issue of Journal on Mechanics of Solids

This is the first issue of the Journal on Mechanics of Solids (JMS). The journal is published by the University of Porto. JMS is an international, peer-reviewed, open access journal dedicated to publishing high-quality, cutting-edge research and review articles in various areas of solid mechanics that contribute to our understanding of the mechanics of solids and structures. JMS covers analytical, theoretical, experimental, and numerical studies that advance the practice of solid mechanics. The journal is expected to receive contributions from various areas of solid mechanics, including (but not limited to) biomechanics, contact mechanics, environmental influences, elasticity and plasticity, micro- and nanomechanics, fracture and damage mechanics, viscoelastic and viscoplastic materials, vibration and dynamics of solids and Structures, mechanics of composites and polymer materials. The scope of the journal also includes fatigue, impact, and creep of solids and structures. JMS also publishes articles on material characterization and mechanical behavior of engineered materials.

Creep experimental study on the lumbar intervertebral disk under vibration compression load.

The intervertebral disk cushions the load generated by human activity and absorbs energy to keep the spine moving steadily. Vibration condition is one of the important causes of disk degeneration. Creep experiments using the sheep lumbar intervertebral disk were carried out under vibration compression. Regularities of the strain of the disk with time were obtained and compared with those of static load. The influence of vibration frequency and time on the creep properties of the intervertebral disk was analyzed. An intervertebral disk three-parameter solid creep constitutive model considering vibration factors was established and the parameters in the model were identified. The results show that the strain of the lumbar intervertebral disk exhibits an exponential relationship with time and is unrelated to static compression or vibration load. Under the same vibration amplitude, the creep increases with vibration frequency and the relationship between them is nonlinear. The vibration frequency has a significant effect on the strain. The creep rate decreases gradually with time and is obviously influenced by vibration frequency at low vibration amplitudes. The creep prediction results obtained using the constitutive model with the time-varying material parameters are in good agreement with the experimental results. The two elastic moduli in the model decrease with time and the viscosity coefficient increases with time.

Early solid additional feeding of suckling rabbits from 3 to 15 days of age

Studies have shown that nutrient requirement of suckling kits is not satisfied, but they can be fed a double quantity of milk (double nursing) resulting in improved BW and weight gain. The aim of our trials was to give additional solid feed during the early suckling period (3 to 15 days of age) when rabbit kits drink exclusively milk. Two experiments were conducted with animals from Pannon Rabbit Breeding Program. In experiment 1 (n=77 does, 734 kits) the does received commercial feed (C) or C pellet supplemented with 0.2 g powdered thyme/kg (CT). Within both dietary groups of the does three groups of litters were formed: no additional solid creep feeding (N); soya bean-based pellet (S); S pellet with 1% added powdered thyme (ST). In group S and ST, cylinder-shaped solid pellets were made. At the beginning (3 days of age) two pieces of pellets were placed daily into the nestbox after nursing. Later on it was increased to six pellets till 15 days of age. The kits consumed the additional solid feed (S and ST), however, it did not affect the BW, weight gain or survival. In experiment 2 (n=30 does, 240 kits) all does consumed commercial feed. The additional feed for kits was based on commercial piglet feed. Three groups were formed: the litters in control group were fed no additional solid feed (K), kits were fed additionally with pellets (8 mm of diameter) based on piglet feed powder, pellet adhesive and water (PI), and extra glycerin powder was added to the mixture of piglet feed powder and water (PG). The experiment lasted from the age of 3 days till 21 days. At the beginning six pellets were placed on the nest material. Later on the amount was gradually increased to 24 pellets till age of 15 days. The kits consumed the pellets. The BW of PI group differed from group PG at age of 5, 9, 12 and 21 days by +7.3%, +6.5%, +5.9%, +4.8%, respectively (P<0.05) and from group K at age of 12 days by +5.9% (P< 0.05). The differences were more expressed at age of 16 and 19 days in favour of group PI (from K by +7.1%, +6.9% and from PG by +5.9%, +5 8%, respectively, P<0.01) and at 21 days of age (from K by +6.2%, P<0.01). To find appropriate composition of creep feed for kits further studies are needed.

Selection of appropriate polyoxymethylene based binder for feedstock material used in powder injection moulding

Polyoxymethylene (POM) has found applications as a binder material in Powder Injection Moulding (PIM) due to its ability to depolymerize rapidly under acidic conditions. Such ability represents an advantage during the binder removal step of PIM. However, currently available POM has high viscosity that can complicate the injection moulding process of parts with complex geometry. For this reason it is necessary to investigate methods of lowering the viscosity of POM-based binders, but without affecting their solid mechanical properties (i.e. creep compliance). In this investigation, the addition of a low molecular weight polymer, and the reduction of the average molecular weight of POM were investigated as possible ways of decreasing the viscosity of PIM binders. The addition of the low molecular weight additive (WAX) caused a small decrease in the viscosity of the POM-based binder and a small increase in its solid creep compliance. On the other hand, lowering the average molecular weight of POM caused a large decrease in viscosity, but also an acceptable increase in creep compliance. Therefore, by selecting an appropriate molecular weight of POM, it is possible to improve the performance of POM-based binders for PIM.

Viscoelastic properties of human normal nucleus pulposus cells

Objective To study the viscoelastic properties of nucleus pulposus (NP) cells from human in vitro. Methods NP was obtained from discarded NP tissue of 3 scoliosis patients aged from 13 to 16 years. Pancreatin and collagenase type Ⅱ were used to digest NP and cells were isolated from NP. Type Ⅱ collagen immunofluorescence and Fan seaing were used to identify NP cells. The micropipette aspiration test was used in combination with a three-parameter viscoelastic solid model to measure the mechanical properties of NP cells. Results The mean diameter of the digested NP cells was ( 15.40 ± 1.83) μm. In response to a prescribed pressure, the NP cells exhibited viscolastic solid creep behavior, which was characterized initially by a jump in displacement followed by a monotony decreasing rate of deformation that generally reached an equilibrium. NP cells were deformed to a length as much as 2 times the radius of the micropipette without completely entering the micropipette. The viscolastic parameters were k1 (0. 101 ±0. 052) kPa, k2 (0. 353 ± 0. 199) kPa, and μ ( 3. 034 ± 1. 843 ) kPa· s, respectively. Only the k1 was positively correlated to the cell diameter (r =-0. 389, P ＜ 0. 05 ). Conclusion Human normal NP cells behave as a typical viscolastic solid creep. Micropipette aspiration technique is a valid method for the study on biomechanics of NP cells. Key words: Nucleus pulposus cells; Biomechanics; Viscoelastic properties

Age-related biomechanical properties of chondrocytes in rabbit knee articular cartilage

To fully demonstrate the alterations about the viscoelastic properties of chondrocytes in rabbit knee articular cartilage. Fifteen New Zealand white rabbits were divided into 3 age groups: young group (1 month), adult group (8 months) and old group (31 months). All rabbits were sacrificed and isolated from knee joint and digested into chondrocytes. The micropipette aspiration combined with Half-space model was used to quantify changes in viscoelastic properties of chondrocytes. Experimental studies have shown that the changes of aspiration length with time in old group were obviously different from young group and adult group. But similar variations were found between the latter two groups. The viscoelastic properties of chondrocytes in old group exhibited a significantly lower instantaneous modulus E0 (0.55 +/- 0.05 kPa), equilibrium modulus E infinity (0.28 +/- 0.04 kPa) and apparent viscosity micro (4.10 +/- 0.61 kPa x s) as compared with young group (0.67 +/- 0.10), (0.37 +/- 0.09), (6.29 +/- 0.92) kPa x s (P < 0.001) versus adult group: (0.65 +/- 0.07), (0.35 +/- 0.05), (6.01 +/- 0.89) kPa x s (P < 0.001). But no difference were found between the latter two groups (P > 0.05). In response to a step pressure, chondrocytes in each group exhibited the viscoelastic solid creep behavior. The viscoelastic properties of chondrocytes markedly decreased in old group.

Mechanical properties of chondrocytes isolated from normal articular cartilage: experiment with rabbit knees

To measure the mechanical properties of chondrocytes of articular cartilage of knee in order to provide relevant technical parameters into the development of cartilage tissue engineering. Eight NZW rabbits were killed, and their bilateral knee joints were taken out. The articular cartilage of the left knees were used for histological study, and articular cartilage of the right knees was digested with 0.4% pronase and 0.025% collagenase type II so as to make isolation of chondrocytes. The viability rate of the isolated chondrocytes was detected by trypan blue staining. The diameters of the chondrocytes in the histological sections and single cell suspension were measured respectively. The mechanical properties of the chondrocytes were determined using micropipette aspiration technique coupled with half-space model. In the normal articular cartilage 4 structural zones were differentiated: tangential, transitional, radial, and calcified zones. The viability rate of chondrocytes was 98.2% on average after isolation. The mean diameter of the chondrocytes in the histological sections was (14.2+/-2.9) microm, not significantly different from that in the single cell suspension [(14.9+/-2.2) microm, t=1.31, P=0.19]. In response to a prescribed pressure, the chondrocytes exhibited viscoelastic solid creep behavior characterized initially by a jump in displacement followed by a monotonically decreasing rate of deformation that generally reached an equilibrium displacement. The cells were observed to deform to a length of as much as three times the radius of the micropipette without completely entering the micropipette. The cells were then extruded from the micropipette and completely recovered. The Young's modulus of the normal chondrocytes was (0.57+/-0.43) kPa, and the k1, k2, and micro of the viscoelastic parameters were (0.37+/-0.07) kPa, (0.29+/-0.04) kPa, and (6.36+/-1.12) kPa-s respectively. The k1 is positively correlated to the cell diameter (r=0.4, P=0.031). Chondrocytes from normal articular cartilage behave as a viscoelastic solid. Micropipette aspiration technique is an efficient method for the study of chondrocyte biomechanics.

Non-linear elastic effects in plasticity: {100} dislocation gliding in aluminum-based alloy

In the general framework of non-linear elasticity, a subtle effect of plasticity recently observed in alloys at room temperature, i.e. the gliding instability of dislocations near axi-symmetrical precipitates, has been explained by means of static atomistic simulations. It is demonstrated that the interaction usually neglected between three sources of strain identified as the dislocations, the external applied strain and the precipitates is responsible for the unusual localized cross-slip of the dislocations from the {111} to {100} planes in zone with the axis of the precipitates. The static atomistic simulations performed at 0 K have clearly shown that the modification of the inter-planar distance in the neighborhood of the precipitates leading to a local modification of the shearing properties is at the origin of this gliding in {100} planes recently observed in Al-Mg-Si alloys 6056. It is believed that the third-order interaction emphasized here plays a key role in many other problems such as creep of solids under irradiation for example.

Micrometer-scale deformation jumps at different stages of creep in solids

Laser interferometry is used to study micrometer-scale creep-strain nonuniformities (jumps) that occur during compression of metals (Ag, Al, Bi, Cu, Pb, Sn, Zn) and LiF: Mg crystals. The strain rate is found to vary periodically. The average magnitude of deformation L over one period and the variation of L with the total strain are determined. Correlations are found to exist between L and the Mg content in the LiF crystals, between L and the grain size in the metals, and between the magnitude of small jumps and the Burgers vector in the metals.

Plastic Deformation of Protein Monolayers

Globular proteins are peculiar solids that display both local stability of their conformation and the ability to undergo large cooperative changes of shape (conformational changes). If one forces a large deformation of the molecule, such that the structure is necessarily changed, it is not obvious whether the deformed globule can still remain a solid or whether it will melt. Is it possible to plastically deform a protein? Here we investigate this question with a micro-mechanical experiment on a small region (∼10 molecules) of a protein monolayer adsorbed on a rigid surface. For the two proteins studied, albumin and myoglobin, we observed that the molecules can be substantially deformed (∼1–2 nm deformation) by comparatively small stresses applied for sufficiently long times. The deformation is irreversible, and the protein remains in the solid state (i.e., displays a nonzero shear modulus). The dynamics of the deformation is approximately logarithmic in time, similar to creep in solids. These results show that globular proteins adsorbed on a surface can be plastically deformed.

Dynamic theory of defects and creep in solids

The dynamic equations of the field theory of defects are used to analyze the creep characteristics. A number of interesting results are obtained, of which some are consistent with the well-known experimental data, whereas others are quite new. In particular, the existence of a critical value of the applied stress and an unstable steady-state creep rate are established, which separate the stable and unstable creep modes and can be of great practical importance.

The effect of farrowing crate heat lamp location on sow and pig patterns of lying and pig survival.

Three experiments were conducted to study sow and pig behavior during the 1st 3 d after birth and pig survival during the 1st 2 wk after farrowing. In Exp. 1, 23 sows were housed in conventional farrowing crates that were divided into five sections: a .5- x 1.5-m front creep section and the remaining area divided into four sections, .75 x 1.05 m each. Air temperature was maintained at 19 degrees C, and a 250-W heat lamp was placed at the right side of the front creep in Treatment 1 (T1), or in the creep at the right side of the sow for Treatment 2 (T2). The percentage of pigs within 8 cm of the sow's trunk was not affected by treatment, but it decreased (P < .001) from 61.8 +/- 3.4% on d 1 to 28.1 +/- 3.5% on d 3. As the percentage of pigs near the sow decreased, the percentage of pigs within the section containing the heat lamp increased (T1, P < .05; T2, P < .10). Experiment 2 involved 15 sows and litters housed as in Exp. 1, except that heat lamps were not provided, and average air temperature was 27.3 +/- .2 degrees C during behavioral observations. Even though the portion of the litter near the sow decreased (P < .001) from d 1 to d 3 (d 1, 57.0 +/- 3.4%; d 2, 42.9 +/- 3.3%; d 3, 31.7 +/- 3.3%), pigs did not concentrate in any specific section as they moved away from the sow. The average number of pigs within the front creep section (Section 1) for the 3-d period was less than (P < .01) the number in any other crate section. Experiment 3 involved 147 sows and tested the effect of solid creep floor covering on pig survival for each of the heat lamp locations used in Exp. 1. Neither heat lamp location nor floor covering affected pig survival. During the 1st 3 d of life, pigs tend to lie near the sow regardless of heat lamp location or air temperature. Heat lamp position and floor covering under the lamp do not affect pig survival.

Performance and behaviour of lactating sows and piglets in crate and multisuckling systems: a study involving European White and Manor Meishan genotypes

AbstractTwo experiments were conducted to compare the performance and behaviour of lactating sows and piglets in farrowing pens with crates or multisuckling systems (group housing of sows and piglets in the second half of lactation). All sows were farrowed in commercial accommodation based on farrowing pens with crates. In experiment 1, fifteen purebred Landrace or Large White sows and litters were recorded in crates as a control (C). Three replicates of six sows and litters were recorded in a multisuckling system (M) in which the sows and litters were group-housed from 2 weeks after farrowing until weaning. Experiment 2 involved 30 Manor Meishan sows (0·25 Meishan genes). The sows and litters were arranged into three treatments and two replicates with five sows and litters in each group. Treatments comprised a control farrowing pen with crate system and two multisuckling systems differing in degree of accessibility of the piglet creep area. Multisuckling 1 (Ml) had a solid creep front with an open doorway (0·5 X 0·9 m) for piglet access. In multisuckling 2 (Ml), the lower 30 cm of the solid creep front was removed to facilitate piglet access and allow visual contact with the sows. Piglets were weaned at 31 days in experiment 1 and 29 days in experiment 2. After weaning, piglets were moved to controiled-environment, fully slatted accommodation and monitored for 7 days in experiment 1 and for 12 days in experiment 2. Mortality rate in the two systems was not significantly different. However, some piglets in the M system were crushed after grouping (0·3 and 0·2 piglets per litter in experiments 1 and 2, respectively). Growth rate was reduced in M piglets in the week after grouping (256, 184 (s.e.d. 21·4) g/day, P &lt; 0·01 for C and M respectively in experiment 1 and 243, 150 and 209 (s.e.d. 12·2) g/day, P &lt; 0·01 for C, Ml and Ml respectively in experiment 2) but was higher after weaning (271, 313 (s.e.d. 35·7) g/day, P &gt; 0·05 for C and M respectively in experiment 1 and 148, 280 and 222 (s.e.d. 15·0) g/day, P &lt; 0·01 for C, Ml and Ml respectively in experiment 2). In consequence, piglet live weight at 1 week after weaning did not differ between treatments (9·33, 9·74 (s.e.d. 0·36) kg for C and M respectively in experiment 1 and 9·30, 914 and 9·53 (s.e.d. Oil) kg for C, Ml and Ml respectively in experiment 2). Sucking behaviour of M piglets in both experiments was severely disrupted (P &lt; 0·01) on the day of grouping and the day after grouping. Despite synchronized suckling, M litters had a high incidence of cross suckling (&gt; 50%) throughout lactation. M piglets spent more time than C outside the creep area, even with a more open creep (Ml). The Meishan sows tended to be more docile and fought less at grouping than the white breeds (0·39 and 1-71 fights per sow per h). Immediately after weaning, C piglets spent more time fighting (8·0 and 1·0 (s.e.d. 0·99) % of time, P &lt; 0·01 for C and M respectively in experiment 1 and 4·51, 0·09 and 0·09 (s.e.d. 019) % of time, P &lt; 0·01 for C, Ml and M2 respectively in experiment 2). These studies demonstrate that, in a multisuckling system, piglets achieved similar overall growth rate to C piglets, since both received checks in growth at different times and for different reasons.

The responsiveness of suckling piglets to solid food presented in different forms

The practice of early weaning of young piglets is associated with a sudden change in both their diet and their method of food acquisition. It can be argued that 4-week-old piglets are neither physiologically nor behaviourally prepared for these rapid changes and the provision of solid creep food is largely ineffective in facilitating adaption to weaning (Fraser et al., 1994). Previous studies which have attempted to promote solid food intake in pre-weaned piglets have tended to focus on dietary factors, such as palatability and digestibility (Bruneau and Chavez, 1995). However for ingestion to occur piglets must first perceive the food items and then establish an attraction to and acceptance of them.

A finite element method for the probabilistic creep of solids

AbstractWe outline here a finite element technique for the creep of solids whose constitutive equation contains one or more random parameters. In contrast to other finite element techniques for the prediction of random structural response, the present method is based upon exact relations from the theory of probability. It yields, at a given value of time, the probability density function for the field variable of interest, e.g. stress or displacement components. The method is illustrated by a simple creeping beam problem, using a power‐law creep constitutive equation. The calculated distributions are found to be highly skewed, and in excellent agreement with the results of Monte Carlo simulation.

Layering of alpine‐Type peridotite and the segregation of partial melt in the upper mantle

For better understanding of the partial melting and melt segregation processes in the upper mantle, we have studied the layered structure of a peridotite mass in Hokkaido, Japan. The layering is characterized by wavy and oscillatory patterns both in terms of bulk rock and mineral chemistry. From the observed linear trends in bulk rock chemistry, we have concluded that such layering was caused by segregation of partial melt in the mantle. Considering the geological and geochemical data, a physical model of melt segregation in the gravity field is put forward. Because permeable flow is strongly coupled with solid creep and compaction, magma waves may be generated by a fluid dynamic oscillation in a partially molten, ascending mantle. A vertical chemical stratification may thus be obtained, starting from a homogeneous mantle. According to the hypothesis, the most depleted part, dunite, is a residue of partial melting, and the least depleted part, plagioclase Iherzolite, represents a melt accumulation region. The partial melt involved was probably picritic in composition.

Elastic creep of stressed solids due to time-dependent changes in elastic properties

The suggestion is made that creep in solids can occur by time-dependent changes in elastic properties. Specific mechanisms include cavity formation and growth, crack nucleation and growth, grain boundary migration in polycrystalline solids with elastically anisotropic grains and the redistribution of the individual phases within a composite. Creep rates by these four mechanisms are analysed and discussed for simple mechanical models. Recommendations are made for the interpretation of creep data in order to clearly separate the contribution of elastic creep from the total creep deformation.

Analysis of low-temperature creep at constant load

Low-temperature creep of solids at constant load is studied in terms of thermally activated process. It is shown that even if the process rate is controlled by only one mechanism of plastic deformation (in particular, the model of cutting forest dislocations is considered), the creep curve begins with a portion of accelerating flow followed by the stage of decreasing strain rate, which turns into the stage of the infinitely increasing flow. Analytically it is also shown that irrespective of the magnitude of the applied stress and the test temperature at P = Const the terminal creep stage is preceded by a certain critical amount of strain, ε crit . The results obtained are compared with the experimental data available.

A Stochastic Model of Creep

AbstractA model of creep in solids is developed in which flow units, identified with dislocation segments in crystals, overcome energy barriers u1 ≦ u ≦ u2 with the aid of thermal activation. Each successful transition of a unit increases or decreases the barrier for the subsequent jump by a stress‐dependent increment. The continuity equation of the Markov process defined by the premise yields activation energy distributions as particular solutions. The distributions are used to derive relations for logarithmic, power‐law, and quasi‐viscous creep. The model delineates the scope of temperature cycling in the determination of activation energies.

Indentation hardness and the creep of solids : A. G. Atkins, A. Silvério and D. Tabor, J. Inst. Metals, 94 (1966) 369–378; 11 figs., 6 tables, 40 refs

Indentation hardness and the creep of solids : A. G. Atkins, A. Silvério and D. Tabor, J. Inst. Metals, 94 (1966) 369–378; 11 figs., 6 tables, 40 refs