Bending and Creep Resistance

Bending strength is the maximum stress a material can withstand before fracturing under a bending load. This property is critically important in structural, construction, composite, and textile materials. Bending strength is typically determined using three-point or four-point bending tests. The material specimen is placed on specific supports, and a load is applied at the center or at defined intervals to identify the point of fracture.

Yield strength is the highest stress a material can endure before undergoing plastic deformation. It is a key mechanical property in metals and composites and one of the fundamental indicators of structural integrity.

Measurement Methods for Bending Strength

Three-Point Bending Test

In this test, a cylindrical or prismatic specimen is placed on two supports, and a load is applied at the exact center. The formulas for bending strength are:

Cylindrical specimen

<span class="katex"><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.4306em;"></span><span class="mord mathnormal" style="margin-right:0.03588em;">σ</span><span class="mord mathnormal">e</span><span class="mord">​</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:0.6833em;"></span><span class="mord mathnormal" style="margin-right:0.13889em;">F</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">⋅</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord mathnormal">L</span><span class="mord">​/</span><span class="mord mathnormal" style="margin-right:0.03588em;">π</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">⋅</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="base"><span class="strut" style="height:0.8141em;"></span><span class="mord"><span class="mord mathnormal" style="margin-right:0.00773em;">R</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.8141em;"><span style="top:-3.063em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">3</span></span></span></span></span></span></span></span></span></span></span>

Prismatic specimen

<span class="katex"><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.4306em;"></span><span class="mord mathnormal" style="margin-right:0.03588em;">σ</span><span class="mord mathnormal">e</span><span class="mord">​</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:0.6833em;"></span><span class="mord">3</span><span class="mord mathnormal" style="margin-right:0.13889em;">F</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">⋅</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="base"><span class="strut" style="height:1.0641em;vertical-align:-0.25em;"></span><span class="mord mathnormal">L</span><span class="mord">/2</span><span class="mord mathnormal">b</span><span class="mord mathnormal">d</span><span class="mord"><span class="mord">​</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.8141em;"><span style="top:-3.063em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">2</span></span></span></span></span></span></span></span></span></span></span>

Here, F is the force at fracture, L is the distance between supports, b is the width, d is the thickness, and R is the radius.

Four-Point Bending Test

In this method, two equal loads are applied to the specimen, resulting in a pure bending condition. The measurement results are more realistic and reliable, but require more complex calculations.

Bending and Yield Strength in Composite Materials

In polyester-based composites, bending strength is directly related to parameters such as resin type (isophthalic or orthophthalic), initiator concentration (e.g., MEKP), and catalyst amount (e.g., cobalt octoate). Experiments have shown that composites containing isophthalic resin exhibit higher bending and tensile strengths compared to those based on orthophthalic resin.

For example:

Bending Strength in Textile Materials

In textile products, bending strength is the primary factor determining fabric stiffness and flexibility. Production parameters such as the number of filaments in yarn significantly affect the bending strength of the fabric. For instance, studies have shown that increasing the number of filaments in the yarn reduces the fabric’s bending resistance (stiffness).

Applications

Bending and yield strength are critical mechanical properties across numerous fields, from materials engineering to textile and structural engineering. These parameters determine the conditions under which a material can be used and can be optimized during production by correctly selecting the proportions of resin, initiator, and additives.